Multiples of a number
Theory
A multiple of a number is what you get when you multiply it by a whole number, so multiples are the numbers you land on when skip counting. A common multiple is a number that appears in the multiples of two numbers.
A multiple of a number is the result of multiplying it by a whole number. The multiples of \(4\) are \(4, 8, 12, 16, 20, \ldots\), which is \(4\times1, 4\times2, 4\times3, \ldots\)
These are the numbers you land on when you skip count by \(4\). Every number has endlessly many multiples, and a number is a multiple of itself.
A common multiple of two numbers appears in both lists. \(30\) is a common multiple of \(5\) and \(6\).
The first five multiples of some numbers — each row is that number's skip-counting pattern:
| Number | 1st | 2nd | 3rd | 4th | 5th |
|---|---|---|---|---|---|
| \(3\) | \(3\) | \(6\) | \(9\) | \(12\) | \(15\) |
| \(4\) | \(4\) | \(8\) | \(12\) | \(16\) | \(20\) |
| \(5\) | \(5\) | \(10\) | \(15\) | \(20\) | \(25\) |
| \(6\) | \(6\) | \(12\) | \(18\) | \(24\) | \(30\) |
How to find multiples
- Multiply the number by \(1, 2, 3, 4, \ldots\), or skip count by it.
- Keep going as far as you need — the list never ends.
- For a common multiple, list the multiples of both numbers and find one that appears in both.
| \(16 + 4\) | \(=\) | \(20\) |
The next multiple of \(4\) is \(20\).
Multiples of \(5\) end in \(0\) or \(5\): \(5\times7 = 35\), \(5\times8 = 40\).
The next one after \(37\) is \(40\).
Multiples of \(6\): \(6, 12, 18, 24, 30\).
\(30\) also ends in \(0\), so it is a multiple of \(5\). Answer: \(30\).
\(7\times14 = 98\) and \(7\times15 = 105\).
\(105\) is too big, so the answer is \(98\).
Common pitfalls
Frequently asked questions
What is a multiple of a number?
What you get when you multiply it by a whole number. The multiples of \(4\) are \(4, 8, 12, 16, 20, \ldots\)
How do you find the multiples of a number?
Skip count by it, or multiply by \(1, 2, 3, \ldots\) The multiples of \(5\) are \(5, 10, 15, 20, 25, \ldots\)
What is a common multiple?
A number that appears in the multiples of two numbers. \(30\) is a common multiple of \(5\) and \(6\).
Is a number a multiple of itself?
Yes. The first multiple of a number is the number itself.
How many multiples does a number have?
Endlessly many — there is no largest multiple, because you can always multiply by a bigger whole number.