LCM for 18, 27 and 36

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

What's the Least Common Multiple (LCM) of 18, 27 and 36?

Answer

LCM of 18, 27 and 36 is
108

(One hundred eight)

108 is the smallest positive integer that 18, 27 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 27 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 27: 3 × 3 × 3 (exponent form: 33)

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

Prime factor182736Highest power
22—2222
332333233

LCM = 22 × 33 = 108

Checking the LCM of 18, 27 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, 27) = (18 × 27) ÷ 9 = 486 ÷ 9 = 54

LCM(54, 36) = (54 × 36) ÷ 18 = 1,944 ÷ 18 = 108

LCM(18, 27, 36) = 108

The pairs may be taken in any order — 27 and 36 first, then 18 — and the answer is the same 108. That is exactly why the two routes on this page agree.

Related Calculations

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 18, 27 and 36? (The answer is: 108). Enter the first number (e.g. '18'), the second (e.g. '27') 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
182127378
182227594
1823271,242
182427216
1825271,350
182627702
18272754
182728756
1827291,566
182730270
1827311,674
182732864
182733594
182734918
1827351,890
182736108
1827371,998
1827381,026
182739702
1827401,080
1827412,214
182742378
1827432,322
1827441,188
182745270
1827461,242
1827472,538
182748432
1827492,646
1827501,350

FAQ

What's the Least Common Multiple (LCM) of 18, 27 and 36?

LCM of 18, 27 and 36 is 108

How to find the LCM of 18, 27 and 36 by prime factorization?

Take every prime that appears in 18, 27 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3³ = 108.

Can you get the LCM of 18, 27 and 36 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 27 is 54, and the LCM of 54 and 36 is 108 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 108 divisible by 18, 27 and 36?

Yes, and by definition it is the smallest positive integer that is: 108 ÷ 18, 108 ÷ 27 and 108 ÷ 36 all come out whole. Any other common multiple of 18, 27 and 36 is a multiple of 108.

See Also