LCM for 6, 11 and 18

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 6, 11 and 18?

Answer

LCM of 6, 11 and 18 is
198

(One hundred ninety-eight)

198 is the smallest positive integer that 6, 11 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 11 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 6: 2 × 3 (exponent form: 2 × 3)

All Prime Factors of 11: 11 (exponent form: 11)

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

Prime factor61118Highest power
22—22
33—3232
11—11—11

LCM = 2 × 32 × 11 = 198

Checking the LCM of 6, 11 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(6, 11) = (6 × 11) ÷ 1 = 66 ÷ 1 = 66

LCM(66, 18) = (66 × 18) ÷ 6 = 1,188 ÷ 6 = 198

LCM(6, 11, 18) = 198

The pairs may be taken in any order — 11 and 18 first, then 6 — and the answer is the same 198. 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 6, 11 and 18? (The answer is: 198). Enter the first number (e.g. '6'), the second (e.g. '11') 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
361166
4611132
5611330
661166
6711462
6811264
6911198
61011330
6111166
61112132
61113858
61114462
61115330
61116528
611171,122
61118198
611191,254
61120660
61121462
6112266
611231,518
61124264
611251,650
61126858
61127594
61128924
611291,914
61130330
611312,046
611321,056

FAQ

What's the Least Common Multiple (LCM) of 6, 11 and 18?

LCM of 6, 11 and 18 is 198

How to find the LCM of 6, 11 and 18 by prime factorization?

Take every prime that appears in 6, 11 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 11 = 198.

Can you get the LCM of 6, 11 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 11 is 66, and the LCM of 66 and 18 is 198 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 198 divisible by 6, 11 and 18?

Yes, and by definition it is the smallest positive integer that is: 198 ÷ 6, 198 ÷ 11 and 198 ÷ 18 all come out whole. Any other common multiple of 6, 11 and 18 is a multiple of 198.

See Also