© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 1
Supplemental Worksheet Problems To Accompany:
The Pre-Algebra Tutor: Volume 2
Section 4– Least Common Multiple
Please watch Section 4 of this DVD before working these problems.
The DVD is located at:
http://www.mathtutordvd.com/products/item67.cfm
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 2
1) Find the least common multiple.
2) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 3
3) Find the least common multiple.
4) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 4
5) Find the least common multiple.
6) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 5
7) Find the least common multiple.
8) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 6
9) Find the least common multiple.
10) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 7
11) Find the least common multiple.
12) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 8
13) Find the least common multiple.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 9
Question
Answer
1) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 2 are 0, 2, 4, 6, 8, 10 , 12, 14 ,16 and so forth.
The first multiples of 7 are 0, 7, 14, 21, 28 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 14 is the lowest multiple of both 2 and 7. Therefore, the least common multiple of 2 and 7 is 14.
Ans: 14
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 10
Question
Answer
2) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 2 are 0, 2, 4, 6, 8, 10 and so forth.
The first multiples of 5 are 0, 5, 10, 15, 20 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 10 is the lowest multiple of both 2 and 5. Therefore, the least common multiple of 2 and 5 is 10.
Ans: 10
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 11
Question
Answer
3) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 4 are 0, 4, 8, 12, 16, 20 and so forth. We can stop at 20 since 4 times 5 equals 20. We know that the least common multiple will not be greater than the two numbers multiplied together.
The first multiples of 5 are 0, 5, 10, 15, 20 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 20 is the lowest multiple of both 4 and 5. Therefore, the least common multiple of 4 and 5 is 20.
Ans: 20
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 12
Question
Answer
4) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 3 are 0, 3, 6, 9, 12, 15 and so forth.
The first multiples of 6 are 0, 6, 12, 18 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 6 is the lowest multiple of both 4 and 5. Therefore, the least common multiple of 3 and 6 is 6.
Ans: 6
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 13
Question
Answer
5) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 9 are 0, 9, 18, 27, 36 and so forth.
The first multiples of 6 are 0, 6, 12, 18, 24 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 18 is the lowest multiple of both 9 and 6. Therefore, the least common multiple of 9 and 6 is 18.
Ans: 18
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 14
Question
Answer
6) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 4 are 0, 4, 8, 12, 16, 20 and so forth.
The first multiples of 7 are 0, 7, 14, 28 and so forth. We can stop at 28 since 4 times 7 equals 28. We know that the least common multiple will not be greater than the two numbers multiplied together.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0). However, there is not a common number on both lists of multiples. The next step is list out additional multiples. We know 28 is as high as we need to go for multiples of 7, so we need to find additional multiples of 4.
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 15
24 and 28 are the next multiples of 4.
Shown in red, we see that 28 is the lowest multiple of both 4 and 7. Therefore, the least common multiple of 4 and 7 is 28.
Ans: 28
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 16
Question
Answer
7) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 5 are 0, 5, 10, 15, 20, 25, 30, 35, 40 and so forth.
The first multiples of 7 are 0, 7, 14, 21, 28, 35, 42 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 35 is the lowest multiple of both 5 and 7. Therefore, the least common multiple of 5 and 7 is 35.
Ans: 35
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 17
Question
Answer
8) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 8 are 0, 8, 16, 24, 32, and so forth.
The first multiples of 6 are 0, 6, 12, 18, 24, 30 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 24 is the lowest multiple of both 8 and 6. Therefore, the least common multiple of 8 and 6 is 24.
Ans: 24
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 18
Question
Answer
9) Find the least common multiple.
Begin.
To find the least common multiple of two numbers, we start listing multiples of both numbers and select the lowest number which is common to both lists.
Multiples of 10 are 0, 10, 20, 30, 40 and so forth.
The first multiples of 15 are 0, 15, 30, 45 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for both. Since we were asked to find the least common multiple, we are looking for the lowest number common to both lists (not including 0).
Shown in red, we see that 30 is the lowest multiple of both 10 and 15. Therefore, the least common multiple of 10 and 15 is 30.
Ans: 30
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 19
Question
Answer
10) Find the least common multiple.
Begin.
To find the least common multiple of three numbers, we start listing multiples of all numbers and selected the lowest number which is common to all three lists.
Multiples of 2 are 0, 2, 4, 6, 8, 10, 12 and so forth.
The first multiples of 5 are 0, 5, 10, 15, 20 and so forth.
The first multiples of 10 are 0, 10, 20, 30 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for all. Since we were asked to find the least common multiple, we are looking for the lowest number common to all lists (not including 0).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 20
Shown in red, we see that 10 is the lowest multiple of 2, 5 and 10. Therefore, the least common multiple of 2, 5 and 10 is 10.
Ans: 10
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 21
Question
Answer
11) Find the least common multiple.
Begin.
To find the least common multiple of three numbers, we start listing multiples of all numbers and select the lowest number which is common to all three lists.
Multiples of 2 are 0, 2, 4, 6, 8, 10, 12 and so forth.
The first multiples of 3 are 0, 3, 6, 9, 12, 15 and so forth.
The first multiples of 4 are 0, 4, 8, 12, 16, 20 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for all. Since we were asked to find the least common multiple, we are looking for the lowest number common to all lists (not including 0).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 22
Shown in red, we see that 12 is the lowest multiple of 2, 3 and 4. Therefore, the least common multiple of 2, 3 and 4 is 12.
Ans: 12
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 23
Question
Answer
12) Find the least common multiple.
Begin.
To find the least common multiple of three numbers, we start listing multiples of all numbers and selected the lowest number which is common to all three lists.
Multiples of 5 are 0, 5, 10, 15, 20, 25, 30 and so forth.
The first multiples of 10 are 0, 10, 20, 30, 40 and so forth.
The first multiples of 15 are 0, 15, 30, 45, 60 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for all. Since we were asked to find the least common multiple, we are looking for the lowest number common to all lists (not including 0).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 24
Shown in red, we see that 30 is the lowest multiple of 5, 10 and 15. Therefore, the least common multiple of 5, 10 and 15 is 30.
Ans: 30
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 25
Question
Answer
13) Find the least common multiple.
Begin.
To find the least common multiple of three numbers, we start listing multiples of all numbers and selected the lowest number which is common to all three lists.
Multiples of 2 are 0, 2, 4, 6, 8, 10, 12 and so forth.
The first multiples of 6 are 0, 6, 12, 18 and so forth.
The first multiples of 4 are 0, 4, 8, 12, 16, 20 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for all. Since we were asked to find the least common multiple, we are looking for the lowest number common to all lists (not including 0).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 26
Shown in red, we see that 12 is the lowest multiple of 2, 6 and 4. Therefore, the least common multiple of 2, 6 and 4 is 12.
Ans: 12
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 27
Question
Answer
12) Find the least common multiple.
Begin.
To find the least common multiple of three numbers, we start listing multiples of all numbers and selected the lowest number which is common to all three lists.
Multiples of 5 are 0, 5, 10, 15, 20, 25, 30 and so forth.
The first multiples of 10 are 0, 10, 20, 30, 40 and so forth.
The first multiples of 15 are 0, 15, 30, 45, 60 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for all. Since we were asked to find the least common multiple, we are looking for the lowest number common to all lists (not including 0).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 28
Shown in red, we see that 30 is the lowest multiple of 5, 10 and 15. Therefore, the least common multiple of 5, 10 and 15 is 30.
Ans: 30
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 29
Question
Answer
13) Find the least common multiple.
Begin.
To find the least common multiple of three numbers, we start listing multiples of all numbers and selected the lowest number which is common to all three lists.
Multiples of 2 are 0, 2, 4, 6, 8, 10, 12 and so forth.
The first multiples of 6 are 0, 6, 12, 18 and so forth.
The first multiples of 4 are 0, 4, 8, 12, 16, 20 and so forth.
Once we have some multiples listed, we can compare the lists to check for any multiples that are common for all. Since we were asked to find the least common multiple, we are looking for the lowest number common to all lists (not including 0).
© 2010 Math TutorDVD.com The Pre-Algebra Tutor: Vol 2 Section 4 – Least Common Multiple
Page 30
Shown in red, we see that 12 is the lowest multiple of 2, 6 and 4. Therefore, the least common multiple of 2, 6 and 4 is 12.
Ans: 12
