Multiple definition
A multiple is a number that is made by multiplying another number by a whole number. For example, the multiples of 5 include 5, 10, 15, 20, 25 and 30. These numbers are all in the 5 times table because they can be made by multiplying 5 by 1, 2, 3, 4, 5, 6 and so on. Multiples are connected to repeated addition, equal groups and times tables.
A useful way to understand multiples is to imagine counting in equal steps. Counting in 3s gives 3, 6, 9, 12, 15 and 18, so these are multiples of 3. Counting in 10s gives 10, 20, 30, 40 and 50, so these are multiples of 10. This is why number lines, arrays and times tables all help students understand what multiples mean.
Multiples are used in number, fractions, ratio, sequences, algebra, factors, divisibility, common multiples and lowest common multiple. At GCSE level, students use multiples to simplify fractions, compare fractions, solve ratio problems, find LCM, identify patterns and work with sequences. They also appear in word problems involving repeated events, packaging, timetables and equal groups.
A factor and a multiple are related but not the same. A factor divides exactly into a number. A multiple is made by multiplying. For example, 4 is a factor of 20 because 20 divided by 4 equals 5. The number 20 is a multiple of 4 because 4 times 5 equals 20. Remembering this difference helps students avoid common mistakes in number questions.
A common multiple is a number that is a multiple of two or more numbers. For example, multiples of 4 include 4, 8, 12, 16, 20 and 24. Multiples of 6 include 6, 12, 18, 24 and 30. Common multiples of 4 and 6 include 12 and 24. The lowest common multiple is the smallest common multiple, so the LCM of 4 and 6 is 12.
Multiples are useful when working with fractions. To add or subtract fractions with different denominators, students often need a common denominator. A common denominator is usually a common multiple of the denominators. For example, to add fractions with denominators 3 and 4, the number 12 is useful because it is a common multiple of both 3 and 4.
Multiples also appear in real-life situations. If buses arrive every 15 minutes, then 15, 30, 45 and 60 minutes are multiples of 15. If packs contain 8 pencils, then 8, 16, 24 and 32 pencils are possible totals from whole packs. These examples show that multiples describe repeated equal amounts, making them useful in practical problem solving.
Related ideas include factors, divisibility, times tables, common multiples, lowest common multiple, prime numbers, fractions and sequences. A clear definition of multiple helps students understand repeated multiplication and recognise number patterns. In exams, list multiples carefully, start from the number itself, and check whether the question is asking for a multiple, a factor, a common multiple or the lowest common multiple.