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

(One hundred twenty-six)

126 is the smallest positive integer that 7, 18 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 7, 18 and 21 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 7: 7 (exponent form: 7)

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

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

Prime factor71821Highest power
2—2—2
3—32332
77—77

LCM = 2 × 32 × 7 = 126

Checking the LCM of 7, 18 and 21 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(7, 18) = (7 × 18) ÷ 1 = 126 ÷ 1 = 126

LCM(126, 21) = (126 × 21) ÷ 21 = 2,646 ÷ 21 = 126

LCM(7, 18, 21) = 126

The pairs may be taken in any order — 18 and 21 first, then 7 — 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 7, 18 and 21? (The answer is: 126). Enter the first number (e.g. '7'), the second (e.g. '18') and the third (e.g. '21'), 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
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, and it is the check this page prints. 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