Multiples Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multiples.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept 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.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Multiples go up forever; factors are limited. A multiple contains the original as a factor.

Common stuck point: Every number is its own smallest multiple (n = n \times 1); students sometimes think multiples must be strictly larger.

Sense of Study hint: Write out the skip-counting sequence: start at the number and keep adding it. The list you build is the multiples.

Worked Examples

Example 1

easy
List the first 6 multiples of 7, and find the 20th multiple of 7.

Solution

  1. 1
    Multiples of 7: 7 \times 1 = 7, 7 \times 2 = 14, 7 \times 3 = 21, 7 \times 4 = 28, 7 \times 5 = 35, 7 \times 6 = 42.
  2. 2
    First 6 multiples: 7, 14, 21, 28, 35, 42.
  3. 3
    20th multiple: 7 \times 20 = 140.

Answer

First 6: 7, 14, 21, 28, 35, 42. The 20th multiple is 140.
Multiples of n are the values n, 2n, 3n, \ldots — the results of multiplying n by positive integers. The kth multiple is simply kn. There are infinitely many multiples of any non-zero integer.

Example 2

medium
Find all multiples of 6 between 50 and 100 (inclusive). How many are there?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Is 252 a multiple of 7? Of 12? Show your reasoning.

Example 2

medium
A light flashes every 4 seconds and a buzzer sounds every 6 seconds. They start together. When will they next coincide? How many times in one minute?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplication