LCM for 12, 18 and 20

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

What's the Least Common Multiple (LCM) of 12, 18 and 20?

Answer

LCM of 12, 18 and 20 is
180

(One hundred eighty)

180 is the smallest positive integer that 12, 18 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 18 and 20 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

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

All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

Prime factor121820Highest power
22222222
3332—32
5——55

LCM = 22 × 32 × 5 = 180

Checking the LCM of 12, 18 and 20 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(12, 18) = (12 × 18) ÷ 6 = 216 ÷ 6 = 36

LCM(36, 20) = (36 × 20) ÷ 4 = 720 ÷ 4 = 180

LCM(12, 18, 20) = 180

The pairs may be taken in any order — 18 and 20 first, then 12 — and the answer is the same 180. That is exactly why the two routes on this page agree.

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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 12, 18 and 20? (The answer is: 180). Enter the first number (e.g. '12'), the second (e.g. '18') and the third (e.g. '20'), 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
51218180
6121836
71218252
8121872
9121836
101218180
111218396
12121836
121318468
121418252
121518180
121618144
121718612
12181836
121819684
121820180
121821252
121822396
121823828
12182472
121825900
121826468
121827108
121828252
1218291,044
121830180
1218311,116
121832288
121833396
121834612

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 20?

LCM of 12, 18 and 20 is 180

How to find the LCM of 12, 18 and 20 by prime factorization?

Take every prime that appears in 12, 18 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 = 180.

Can you get the LCM of 12, 18 and 20 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 18 is 36, and the LCM of 36 and 20 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 12, 18 and 20?

Yes, and by definition it is the smallest positive integer that is: 180 ÷ 12, 180 ÷ 18 and 180 ÷ 20 all come out whole. Any other common multiple of 12, 18 and 20 is a multiple of 180.

See Also