LCM for 12, 22 and 40

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 12, 22 and 40?

Answer

LCM of 12, 22 and 40 is
1,320

(One thousand three hundred twenty)

1,320 is the smallest positive integer that 12, 22 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 12, 22 and 40 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 12: 2 × 2 × 3 (exponent form: 22 × 3)

All Prime Factors of 22: 2 × 11 (exponent form: 2 × 11)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

Prime factor122240Highest power
22222323
33——3
5——55
11—11—11

LCM = 23 × 3 × 5 × 11 = 1,320

Checking the LCM of 12, 22 and 40 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(12, 22) = (12 × 22) ÷ 2 = 264 ÷ 2 = 132

LCM(132, 40) = (132 × 40) ÷ 4 = 5,280 ÷ 4 = 1,320

LCM(12, 22, 40) = 1,320

The pairs may be taken in any order — 22 and 40 first, then 12 — and the answer is the same 1,320. That is exactly why the two routes on this page agree.

Related Calculations

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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 12, 22 and 40? (The answer is: 1,320). Enter the first number (e.g. '12'), the second (e.g. '22') and the third (e.g. '40'), 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
1222253,300
1222261,716
1222271,188
122228924
1222293,828
122230660
1222314,092
1222321,056
122233132
1222342,244
1222354,620
122236396
1222374,884
1222382,508
1222391,716
1222401,320
1222415,412
122242924
1222435,676
122244132
1222451,980
1222463,036
1222476,204
122248528
1222496,468
1222503,300
1222512,244
1222521,716
1222536,996
1222541,188

FAQ

What's the Least Common Multiple (LCM) of 12, 22 and 40?

LCM of 12, 22 and 40 is 1,320

How to find the LCM of 12, 22 and 40 by prime factorization?

Take every prime that appears in 12, 22 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 11 = 1,320.

Can you get the LCM of 12, 22 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 12 and 22 is 132, and the LCM of 132 and 40 is 1,320 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,320 divisible by 12, 22 and 40?

Yes, and by definition it is the smallest positive integer that is: 1,320 ÷ 12, 1,320 ÷ 22 and 1,320 ÷ 40 all come out whole. Any other common multiple of 12, 22 and 40 is a multiple of 1,320.

See Also