LCM for 7, 18 and 21

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

What's the Least Common Multiple (LCM) of 7, 18 and 21?

Answer

LCM of 7, 18 and 21 is
126

First common multiples: 126, 252, 378, …

126 is divisible by all three: 126 ÷ 7 = 18, 126 ÷ 18 = 7, 126 ÷ 21 = 6 — and 18, 7 and 6 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/7 by 18 and of y/18 by 7 and of z/21 by 6.

7 — prime

18 = 2 × 32

21 = 3 × 7

Prime71821Highest power
2—2—2
3—32332
77—77

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2 × 32 × 7 = 126

More with these numbers

Related Calculations

See Also

LCM Table

1st2nd3rdLCM
6718126
7718126
7818504
7918126
71018630
711181,386
71218252
713181,638
71418126
71518630
716181,008
717182,142
71818126
718192,394
718201,260
71821126
718221,386
718232,898
71824504
718253,150
718261,638
71827378
71828252
718293,654
71830630
718313,906
718322,016
718331,386
718342,142
71835630

FAQ

What's the Least Common Multiple (LCM) of 7, 18 and 21?

LCM of 7, 18 and 21 is 126

How to find the LCM of 7, 18 and 21 by prime factorization?

Take every prime that appears in 7, 18 and 21 to the highest power it reaches in any one of them and multiply: 2 × 3² × 7 = 126.

Can you get the LCM of 7, 18 and 21 two numbers at a time?

Yes. The LCM of 7 and 18 is 126, and the LCM of 126 and 21 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 7, 18 and 21?

Yes, and by definition it is the smallest positive integer that is: 126 ÷ 7, 126 ÷ 18 and 126 ÷ 21 all come out whole. Any other common multiple of 7, 18 and 21 is a multiple of 126.

See Also