Number sequences with multiples
Theory
Number sequences with multiples is a Year 4 maths pattern skill: building lists like \(8, 16, 24, 32\) by skip counting in equal steps, spotting multiples on a number line and hundred chart, working out the next term and the nth multiple, and finding a common multiple of two numbers. This page explains the step rule, the link to times tables, and how to test whether a number belongs in a sequence. Curriculum: VC2M4N02 / AC9M4N09, AC9M4A02.
A multiple of a number is what you land on when you count in equal steps of that number. The multiples of 8 are \(8, 16, 24, 32, 40, \ldots\) — the same as the eight times table. The list never ends, because you can always take one more step.
The step between the terms is the number itself, so the multiples of 8 go up by 8 each time. To find the next term, add the step. A number sequence like \(9, 18, 27, 36\) is just the multiples of one number written in order.
The nth multiple is that many steps from the start, which is the same as a times fact: the 3rd multiple of 9 is \(3 \times 9 = 27\). A common multiple is a number that appears in two lists — \(15\) is a common multiple of 3 and 5.
Number sequences with multiples do not need formulas, but these facts help you build and check them.
How to work with a sequence of multiples
- Find the step. Take one term away from the next, like \(16 - 8 = 8\). The step is the number you are counting by.
- Move along. Add the step to go to the next term, or subtract it to go back one term.
- Jump to any multiple. To find the nth multiple, multiply: the nth multiple is \(n \times \text{the number}\), like \(6 \times 5 = 30\).
| \(\text{step}\) | \(=\) | \(36 - 27 = 9\) |
| \(54 + 9\) | \(=\) | \(63\) |
The next multiple of 9 is \(63\).
| \(\text{each jump}\) | \(=\) | \(+6\) |
| \(30 + 6\) | \(=\) | \(36\) |
The missing number is \(36\). Check: \(36 + 6 = 42\).
| \(5,\ 10,\ 15,\ 20,\ 25,\ 30\) | ||
| \(6 \times 5\) | \(=\) | \(30\) |
The 6th multiple of 5 is \(30\).
| \(\text{3s}\) | \(:\) | \(3,\ 6,\ 9,\ 12,\ 15\) |
| \(\text{5s}\) | \(:\) | \(5,\ 10,\ 15\) |
\(15\) is in both lists, so it is the smallest common multiple.
Common pitfalls
Frequently asked questions
What is a multiple?
A multiple of a number is what you land on when you count in equal steps of that number. The multiples of 8 are \(8, 16, 24, 32, 40\), which is the same as the eight times table.
How do you find the next number in a sequence of multiples?
Find the step by taking one term away from the next, then add that step to the last term. For \(27, 36, 45\) the step is 9, so the next number is \(45 + 9 = 54\).
How do you find the 6th multiple of a number?
Multiply the count by the number. The 6th multiple of 5 is \(6 \times 5 = 30\). You can also skip count six steps: \(5, 10, 15, 20, 25, 30\).
How do you know if a number is a multiple of 5?
A multiple of 5 ends in 0 or 5, because you count \(5, 10, 15, 20\) and so on. To be sure, keep skip counting by 5 and check whether a step lands on the number.
What is a common multiple?
A common multiple is a number that appears in the multiples list of two numbers. \(15\) is a common multiple of 3 and 5, because \(5 \times 3 = 15\) and \(3 \times 5 = 15\), so it is in both lists.
What is the difference between a multiple and a factor?
A multiple comes from counting in steps, like the multiples of 4 being \(4, 8, 12\). A factor divides exactly into a number, like 4 being a factor of 12. So \(12\) is a multiple of 4, and 4 is a factor of 12.