LCM for 20, 25 and 40

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What's the Least Common Multiple (LCM) of 20, 25 and 40?

Answer

LCM of 20, 25 and 40 is
200

First common multiples: 200, 400, 600, …

200 is divisible by all three: 200 ÷ 20 = 10, 200 ÷ 25 = 8, 200 ÷ 40 = 5 — and 10, 8 and 5 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/20 by 10 and of y/25 by 8 and of z/40 by 5.

20 = 22 × 5

25 = 52

40 = 23 × 5

Prime202540Highest power
222—2323
5552552

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

LCM = 23 × 52 = 200

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LCM Table

1st2nd3rdLCM
202525100
2025261,300
2025272,700
202528700
2025292,900
202530300
2025313,100
202532800
2025333,300
2025341,700
202535700
202536900
2025373,700
2025381,900
2025393,900
202540200
2025414,100
2025422,100
2025434,300
2025441,100
202545900
2025462,300
2025474,700
2025481,200
2025494,900
202550100
2025515,100
2025521,300
2025535,300
2025542,700

FAQ

What's the Least Common Multiple (LCM) of 20, 25 and 40?

LCM of 20, 25 and 40 is 200

How to find the LCM of 20, 25 and 40 by prime factorization?

Take every prime that appears in 20, 25 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 5² = 200.

Can you get the LCM of 20, 25 and 40 two numbers at a time?

Yes. The LCM of 20 and 25 is 100, and the LCM of 100 and 40 is 200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 200 divisible by 20, 25 and 40?

Yes, and by definition it is the smallest positive integer that is: 200 ÷ 20, 200 ÷ 25 and 200 ÷ 40 all come out whole. Any other common multiple of 20, 25 and 40 is a multiple of 200.

See Also