Multiples and times tables

Multiples and times tables

A multiple of a number is what you get by multiplying it by 1, 2, 3, 4, … In other words, multiples of N are just the N times table.

Generating multiples

The easiest way: start at the number and keep adding it to itself.

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, …

This is the same as saying 1×7, 2×7, 3×7, … — so the multiples of 7 are the 7-times table.

Is this number a multiple?

To check whether A is a multiple of B, divide. If the answer comes out a whole number with no remainder, A is a multiple of B.

Is 84 a multiple of 6?

84 ÷ 6 = 14 (no remainder). Yes — 84 is the 14th multiple of 6.

Is 84 a multiple of 5?

84 ÷ 5 = 16 r 4. No — 84 is not in the 5 times table.

Common multiples

A common multiple of two numbers is a number that's in both their lists.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, …

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, …

The first few common multiples of 4 and 6 are 12, 24, 36, 48, … The smallest one (12) has its own name in later grades: the least common multiple.

Why multiples are useful

Multiples turn up everywhere:

  • Schedule problems. A bus comes every 5 minutes, another every 7 minutes. They leave together at 8:00. When will they both be at the stop at the same time? — find a common multiple of 5 and 7. The answer is 35 minutes later, at 8:35.
  • Dividing into groups. You can split 36 sweets evenly among 4, 6, 9 or 12 children, because 36 is a multiple of all those numbers.

Spotting multiples at a glance

Some multiples are easy to spot from the digits:

  • Multiples of 2 end in 0, 2, 4, 6 or 8.
  • Multiples of 5 end in 0 or 5.
  • Multiples of 10 end in 0.
  • Multiples of 9 have digits that add up to a multiple of 9 (you'll learn this trick more in Year 5).

What's next

Try it out