LCM Calculator

Find the least common multiple (LCM) of two or more whole numbers, with prime-factor working.

Whole numbers	4, 6, 10

Whole numbers

Separate with commas or spaces.

Least common multiple

60 is the smallest positive number that all of 4, 6, 10 divide into.

Exact. Checked exactly.

Method: Prime factorisation
Worked out with: AllCalcHub whole-number arithmetic
Check: Every step recomputed with exact fractions

GCF: 2

1
Break each number into prime factors
4 = 2²; 6 = 2 × 3; 10 = 2 × 5
2
Multiply every prime that appears, each to its highest power
2² × 3 × 5 = 60

Ladder (common division) method: LCM = 2 × 2 × 3 × 5 = 60

Divide by	Number 1	Number 2	Number 3
2	4	6	10
	2	3	5

About the LCM Calculator

The least common multiple is the smallest positive number that every number in the set divides into. It's used to add fractions with different denominators and to work out when repeating events line up.

The formula

LCM(a, b) = |a × b| ÷ GCF(a, b)

GCF: greatest common factor

For more than two numbers, apply it pairwise: LCM(a, b, c) = LCM(LCM(a, b), c).

Worked example

LCM of 4, 6 and 10

4 = 2², 6 = 2 × 3, 10 = 2 × 5
Highest powers: 2² × 3 × 5 = 60

Questions people ask

Why do I need the LCM to add fractions?

It's the lowest common denominator, so you can rewrite each fraction with it and add the numerators.

Can the LCM be smaller than the numbers?

No. It's always at least as large as the largest number.