What Is A Multiple: Explained For Primary School

Make learning what is a multiple, simple for KS1 and KS2 children. Here is a step by step guide to support teaching multiples in Primary School. A secure knowledge of times tables is essential in calculating multiples. 

What is a multiple?

A multiple of a number is the result when that number is multiplied by an integer. Examples of multiple of 14 could be 14 (14 x 1), 28 (14 x 2) or 140 (14 x 10). The definition of multiple can also be described as numbers in a given times table – for example, 5, 10, 15 and 20 are all in the 5 times table; they are also all multiples of 5. Even numbers are all multiples of 2. There is a multiple of every number. 

Children often confuse multiples with factors, so it is important they learn about the difference between factors and multiples.

When do children learn about multiples in the national curriculum?

Children are expected to know the first 12 multiples of the numbers 1-12 by the end of Year 4, when they will have their times table check this is gradually taught from the beginning of

Year 1:

• Count in multiples (also known as ‘skip counting’) of twos, fives and tens

Year 2:

• Count in multiples of three to support later understanding of a third

Year 3:

• Count from 0 in multiples of 4, 8, 50 and 100 (pupils now use multiples of 2, 3, 4, 5, 8, 10, 50 and 100)

Year 4:

• Count in multiples of 6, 7, 9, 25 and 1000
• Use factors and multiples to recognise equivalent fractions and simplify where appropriate

Alongside the regular times tables, multiples of 25, 50, 100 and 1000 are also explicitly taught as these are useful when working with fractions decimals percentages and units of measurement

Year 5:

• Identify multiples and factors
• Solve problems involving multiplication and division including using their knowledge of factors and multiples, square numbers and cube numbers

Year 6: 

• Identify common factors, common multiples and prime numbers
• Use common multiples to express fractions in the same denomination
• Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

See also: Long multiplication method & Long multiplication

What is the lowest common multiple?

The lowest common multiple (LCM), also referred to as the least common multiple, is the smallest multiple shared between two given numbers. For example, the lowest common multiple of 9 and 12 is 36 as it is the smallest multiple that both given numbers share (9 x 4 = 36 and 12 x 3 = 36). Lowest common multiples can be used to express fractions in the same denomination, which is useful when they are being added or subtracted.

How do multiples relate to other areas of maths?

Multiples and factors are often taught together: whilst factors are the result when you divide a number by an integer (with no remainder), multiples are the result when you multiply a number by an integer. In Year 5 geometry, children are taught multiples of 90 degrees (90 = quarter turn; 180 = half a turn, or a straight line; 270 = three-quarter turn; 360 = full turn, or a circle). As previously mentioned, finding common multiples are also useful when expressing fractions in the same denomination. 

Multiples of numbers in real life

Multiples are useful when organising a number into groups – for example, 25 is a multiple of 5: 25 children could be organised into groups of 5; 25p could be paid in 5ps. Common multiples are also useful in real life contexts – for example, if burgers come in packs of 8 but burger buns come in packs of 6, finding a common multiple (24) would help you work out how many of each pack to buy (3 and 4 respectively) without wasting any.

5 multiple practice questions and answers

• 1. What’s the lowest common multiple of 8 and 12?
• 2. Chen uses these digit cards: 5 6 9. She makes a two-digit number and a one-digit number. She multiplies them together. Her answer is a multiple of 10. What could Chen’s multiplication be? (SATs 2017)
• 3. Write all the common multiples of 3 and 8 that are less than 50. (SATs 2016)
• 4. In the circles, write a multiple that belongs to each set. One has been done for you. (SATs 2016 sample)

• 5. Here is a diagram for sorting numbers. Write one number in each box. One is done for you. (SATs 2016 sample)

Answers:

1. 24
2. 96 x 5
3. 24, 48
4. a) 120, 140, 160 or 180
   b) 210, 240 or 270
   c) 320 or 360
5. Top right: 3, 6, 9, 12, 18 etc.
   Bottom left: 5, 10, 20, 25, 35 etc.
   Bottom right: 1, 2, 4, 7, 8 etc.

Looking for more multiplication resources? Take a look at our collection of multiplication worksheets.

Looking for more advice on how to explain other mathematical concepts to your students? Take a look at our Primary Maths Dictionary.

Further Reading:

• Teaching Addition and Subtraction KS2 
• What is a Prime Number and Prime Factor?
• The Highest Common Factor