LCM for 24, 36 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 24, 36 and 40?

Answer

LCM of 24, 36 and 40 is
360

(Three hundred sixty)

360 is the smallest positive integer that 24, 36 and 40 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 24, 36 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

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

Prime factor243640Highest power
223222323
3332—32
5——55

LCM = 23 × 32 × 5 = 360

Checking the LCM of 24, 36 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(24, 36) = (24 × 36) ÷ 12 = 864 ÷ 12 = 72

LCM(72, 40) = (72 × 40) ÷ 8 = 2,880 ÷ 8 = 360

LCM(24, 36, 40) = 360

The pairs may be taken in any order — 36 and 40 first, then 24 — and the answer is the same 360. 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 24, 36 and 40? (The answer is: 360). Enter the first number (e.g. '24'), the second (e.g. '36') 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
2425361,800
242636936
242736216
242836504
2429362,088
243036360
2431362,232
243236288
243336792
2434361,224
2435362,520
24363672
2436372,664
2436381,368
243639936
243640360
2436412,952
243642504
2436433,096
243644792
243645360
2436461,656
2436473,384
243648144
2436493,528
2436501,800
2436511,224
243652936
2436533,816
243654216

FAQ

What's the Least Common Multiple (LCM) of 24, 36 and 40?

LCM of 24, 36 and 40 is 360

How to find the LCM of 24, 36 and 40 by prime factorization?

Take every prime that appears in 24, 36 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 = 360.

Can you get the LCM of 24, 36 and 40 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 24 and 36 is 72, and the LCM of 72 and 40 is 360 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 360 divisible by 24, 36 and 40?

Yes, and by definition it is the smallest positive integer that is: 360 ÷ 24, 360 ÷ 36 and 360 ÷ 40 all come out whole. Any other common multiple of 24, 36 and 40 is a multiple of 360.

See Also