LCM for 10, 12 and 18

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

What's the Least Common Multiple (LCM) of 10, 12 and 18?

Answer

LCM of 10, 12 and 18 is
180

(One hundred eighty)

180 is the smallest positive integer that 10, 12 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 12 and 18 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 18: 2 × 3 × 3 (exponent form: 2 × 32)

Prime factor101218Highest power
2222222
3—33232
55——5

LCM = 22 × 32 × 5 = 180

Checking the LCM of 10, 12 and 18 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(10, 12) = (10 × 12) ÷ 2 = 120 ÷ 2 = 60

LCM(60, 18) = (60 × 18) ÷ 6 = 1,080 ÷ 6 = 180

LCM(10, 12, 18) = 180

The pairs may be taken in any order — 12 and 18 first, then 10 — and the answer is the same 180. That is exactly why the two routes on this page agree.

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See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 10, 12 and 18? (The answer is: 180). Enter the first number (e.g. '10'), the second (e.g. '12') and the third (e.g. '18'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
3101260
4101260
5101260
6101260
71012420
81012120
91012180
10101260
101112660
10121260
101213780
101214420
10121560
101216240
1012171,020
101218180
1012191,140
10122060
101221420
101222660
1012231,380
101224120
101225300
101226780
101227540
101228420
1012291,740
10123060
1012311,860
101232480

FAQ

What's the Least Common Multiple (LCM) of 10, 12 and 18?

LCM of 10, 12 and 18 is 180

How to find the LCM of 10, 12 and 18 by prime factorization?

Take every prime that appears in 10, 12 and 18 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 10, 12 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 12 is 60, and the LCM of 60 and 18 is 180 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 180 divisible by 10, 12 and 18?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 10, 180 ÷ 12 and 180 ÷ 18 all come out whole. Any other common multiple of 10, 12 and 18 is a multiple of 180.

See Also