What Are Multiples?

A multiple of a number is what you get when you multiply that number by any whole number (1, 2, 3, 4, ...). Multiples are like the number's times table — they go on forever.

Multiplication tables — which are really just organised lists of multiples — are some of the oldest surviving mathematical documents in existence. Clay tablets from the Old Babylonian period, dated to around 1800 BCE, record tables of multiples for the base-60 number system the Babylonians used, the very same system that still gives us 60 minutes in an hour and 360 degrees in a circle today. The habit of listing out a number’s multiples to spot patterns is, in other words, nearly 4,000 years old.

Formal Definition

M is a multiple of N if M = N × k for some positive whole number k.

Examples

Number	First 8 Multiples
3	3, 6, 9, 12, 15, 18, 21, 24
7	7, 14, 21, 28, 35, 42, 49, 56
12	12, 24, 36, 48, 60, 72, 84, 96
0.5	0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4

Key Properties of Multiples

The first multiple of any number is the number itself (n × 1 = n).
Multiples are always equal to or greater than the number.
There are infinitely many multiples of any number.
Every number is a multiple of 1.
Zero is technically a multiple of every number (n × 0 = 0) — but is usually excluded from lists.

Multiples vs Factors – Side by Side

Property	Factors	Multiples
Relationship	Divide INTO the number	Number divides INTO them
Size	≤ the number	≥ the number
Count	Finite	Infinite
Example (6)	1, 2, 3, 6	6, 12, 18, 24...

Multiples in Real Life

Clocks: Minutes are multiples of 1; quarter hours are multiples of 15.
Music: Beats repeat in multiples of the time signature.
Packing: Boxes of 12 — stock levels are multiples of 12.

Key Takeaways

Multiples = the number × 1, 2, 3, 4... (times table extended infinitely).
A number is a multiple of its own factors.
Multiples are always ≥ the original number (excluding 0).
Finding common multiples leads to the LCM.

Practice: Multiples

Multiples Question