Practice Least Common Multiple in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

The smallest positive integer that is divisible by each of two or more given numbers—where their multiples first coincide.

The first number that appears in both times tables—where two counting sequences land on the same value.

Showing a random 20 of 50 problems.

Example 1

medium

Subtract:

\dfrac{5}{6} - \dfrac{3}{8}

using LCM as denominator.

Example 2

medium

Two bells ring every 12 and 18 minutes. After how many minutes do they ring together?

Example 3

medium

Three buses leave the station every

15

20

, and

30

minutes respectively. If they leave together at noon, when do they next all leave together?

Example 4

medium

Find the LCM of

16

and

24

Example 5

challenge

Two gears have 14 and 21 teeth. How many rotations of the smaller gear until both return to start together?

Example 6

easy

Find the LCM of

6

and

8

Example 7

medium

Find the LCM of

4

6

, and

10

Example 8

medium

Find the LCM of

10

and

15

using prime factorization.

Example 9

easy

Find the LCM of

5

and

10

Example 10

medium

Find the LCM of

9

and

15

Example 11

easy

Find the LCM of

4

and

10

by listing multiples.

Example 12

hard

\gcd(a, b) = 12

and

\text{LCM}(a, b) = 180

. If

a = 36

, find

b

Example 13

challenge

Find the smallest number that leaves remainder 0 when divided by 6, 8, and 9.

Example 14

easy

Find the LCM of

6

and

9

Example 15

hard

Find the smallest positive integer divisible by

4

5

6

, and

9

Example 16

medium

Use prime factorization to find the LCM of

12

and

18

Example 17

easy

Find the LCM of

3

and

5

Example 18

medium

Find the LCM of

8

and

20

using prime factorization.

Example 19

easy

Find the LCM of

7

and

14

Example 20

medium

Find the LCM of

14

and

21

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Related Concepts

Multiples Adding Fractions