Practice Multiples in Math

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

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Quick Recap

Numbers obtained by multiplying a given number by positive integers: the skip-counting sequence $n, 2n, 3n, 4n, \ldots$

Skip-counting produces multiples: counting by 3s gives 3, 6, 9, 12... — those are the multiples of 3.

Showing a random 20 of 50 problems.

Example 1

medium

Three friends jog around a track. They finish a lap every

4,6,

and

8

minutes. If they start together, when do they all finish a lap at the same time again?

Example 2

medium

What is the smallest positive multiple of

12

that is also a multiple of

20

Example 3

easy

20

a multiple of

5

Example 4

easy

List the first six multiples of

11

. What pattern do you see in the digits?

Example 5

challenge

Find the smallest positive integer that is a multiple of

2,3,4,5,6,7,8,9,

and

10

Example 6

easy

27

a multiple of

3

Example 7

medium

Find the least common multiple of

4

and

6

Example 8

hard

A number

N

is a multiple of

6

and ends in

0

. The smallest such

N

greater than

50

is what?

Example 9

easy

Which of

14, 15, 16

is a multiple of

4

Example 10

hard

Show that the sum of any three consecutive multiples of

5

is divisible by

15

Example 11

easy

Do the multiples of

7

ever stop?

Example 12

easy

List the multiples of

9

less than

50

Example 13

medium

How many multiples of

4

are there between

1

and

40

inclusive?

Example 14

easy

List the first four multiples of

3

Example 15

hard

A multiple of

7

between

200

and

300

has digits that sum to

9

. Find it.

Example 16

medium

How many multiples of

8

are there between

50

and

150

inclusive?

Example 17

challenge

Prove that every multiple of

6

is also a multiple of both

2

and

3

Example 18

easy

List the multiples of

10

up to

50

Example 19

easy

List the first

6

multiples of

7

, and find the

20

th multiple of

7

Example 20

hard

Find all multiples of

7

between

1

and

200

whose digits sum to a multiple of

7

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Related Concepts

Multiplication Least Common Multiple Divisibility Intuition