LCM for 12, 18 and 36

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 12, 18 and 36?

Answer

LCM of 12, 18 and 36 is
36

(Thirty-six)

36 is the smallest positive integer that 12, 18 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 18 and 36 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 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor121836Highest power
22222222
33323232

LCM = 22 × 32 = 36

Checking the LCM of 12, 18 and 36 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, 36) = (36 × 36) ÷ 36 = 1,296 ÷ 36 = 36

LCM(12, 18, 36) = 36

The pairs may be taken in any order — 18 and 36 first, then 12 — and the answer is the same 36. That is exactly why the two routes on this page agree.

Related Calculations

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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 36? (The answer is: 36). Enter the first number (e.g. '12'), the second (e.g. '18') and the third (e.g. '36'), 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
121821252
121822396
121823828
12182472
121825900
121826468
121827108
121828252
1218291,044
121830180
1218311,116
121832288
121833396
121834612
1218351,260
12183636
1218371,332
121838684
121839468
121840360
1218411,476
121842252
1218431,548
121844396
121845180
121846828
1218471,692
121848144
1218491,764
121850900

FAQ

What's the Least Common Multiple (LCM) of 12, 18 and 36?

LCM of 12, 18 and 36 is 36

How to find the LCM of 12, 18 and 36 by prime factorization?

Take every prime that appears in 12, 18 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² = 36.

Can you get the LCM of 12, 18 and 36 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 36 is 36 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 36 divisible by 12, 18 and 36?

Yes, and by definition it is the smallest positive integer that is: 36 ÷ 12, 36 ÷ 18 and 36 ÷ 36 all come out whole. Any other common multiple of 12, 18 and 36 is a multiple of 36.

See Also