LCM for 18, 21 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 18, 21 and 36?

Answer

LCM of 18, 21 and 36 is
252

(Two hundred fifty-two)

252 is the smallest positive integer that 18, 21 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 21 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

Prime factor182136Highest power
22—2222
33233232
7—7—7

LCM = 22 × 32 × 7 = 252

Checking the LCM of 18, 21 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(18, 21) = (18 × 21) ÷ 3 = 378 ÷ 3 = 126

LCM(126, 36) = (126 × 36) ÷ 18 = 4,536 ÷ 18 = 252

LCM(18, 21, 36) = 252

The pairs may be taken in any order — 21 and 36 first, then 18 — and the answer is the same 252. 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 18, 21 and 36? (The answer is: 252). Enter the first number (e.g. '18'), the second (e.g. '21') 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
182121126
1821221,386
1821232,898
182124504
1821253,150
1821261,638
182127378
182128252
1821293,654
182130630
1821313,906
1821322,016
1821331,386
1821342,142
182135630
182136252
1821374,662
1821382,394
1821391,638
1821402,520
1821415,166
182142126
1821435,418
1821442,772
182145630
1821462,898
1821475,922
1821481,008
182149882
1821503,150

FAQ

What's the Least Common Multiple (LCM) of 18, 21 and 36?

LCM of 18, 21 and 36 is 252

How to find the LCM of 18, 21 and 36 by prime factorization?

Take every prime that appears in 18, 21 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

Can you get the LCM of 18, 21 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 21 is 126, and the LCM of 126 and 36 is 252 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 252 divisible by 18, 21 and 36?

Yes, and by definition it is the smallest positive integer that is: 252 ÷ 18, 252 ÷ 21 and 252 ÷ 36 all come out whole. Any other common multiple of 18, 21 and 36 is a multiple of 252.

See Also