LCM for 6, 14 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, 14 and 18?

Answer

LCM of 6, 14 and 18 is
126

(One hundred twenty-six)

126 is the smallest positive integer that 6, 14 and 18 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 6, 14 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 14: 2 × 7 (exponent form: 2 × 7)

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

Prime factor61418Highest power
22222
33—3232
7—7—7

LCM = 2 × 32 × 7 = 126

Checking the LCM of 6, 14 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, 14) = (6 × 14) ÷ 2 = 84 ÷ 2 = 42

LCM(42, 18) = (42 × 18) ÷ 6 = 756 ÷ 6 = 126

LCM(6, 14, 18) = 126

The pairs may be taken in any order — 14 and 18 first, then 6 — and the answer is the same 126. 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, 14 and 18? (The answer is: 126). Enter the first number (e.g. '6'), the second (e.g. '14') 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
361442
461484
5614210
661442
671442
6814168
6914126
61014210
61114462
6121484
61314546
6141442
61415210
61416336
61417714
61418126
61419798
61420420
6142142
61422462
61423966
61424168
614251,050
61426546
61427378
6142884
614291,218
61430210
614311,302
61432672

FAQ

What's the Least Common Multiple (LCM) of 6, 14 and 18?

LCM of 6, 14 and 18 is 126

How to find the LCM of 6, 14 and 18 by prime factorization?

Take every prime that appears in 6, 14 and 18 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

Can you get the LCM of 6, 14 and 18 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 6 and 14 is 42, and the LCM of 42 and 18 is 126 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 126 divisible by 6, 14 and 18?

Yes, and by definition it is the smallest positive integer that is: 126 ÷ 6, 126 ÷ 14 and 126 ÷ 18 all come out whole. Any other common multiple of 6, 14 and 18 is a multiple of 126.

See Also