LCM for 20, 25 and 30

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What's the Least Common Multiple (LCM) of 20, 25 and 30?

Answer

LCM of 20, 25 and 30 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 20 = 15, 300 ÷ 25 = 12, 300 ÷ 30 = 10 — and 15, 12 and 10 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 15 and of y/25 by 12 and of z/30 by 10.

20 = 22 × 5

25 = 52

30 = 2 × 3 × 5

Prime202530Highest power
222—222
3——33
5552552

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

LCM = 22 × 3 × 52 = 300

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LCM Table

1st2nd3rdLCM
152025300
162025400
1720251,700
182025900
1920251,900
202025100
2021252,100
2022251,100
2023252,300
202425600
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

FAQ

What's the Least Common Multiple (LCM) of 20, 25 and 30?

LCM of 20, 25 and 30 is 300

How to find the LCM of 20, 25 and 30 by prime factorization?

Take every prime that appears in 20, 25 and 30 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 20, 25 and 30 two numbers at a time?

Yes. The LCM of 20 and 25 is 100, and the LCM of 100 and 30 is 300 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 300 divisible by 20, 25 and 30?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 20, 300 ÷ 25 and 300 ÷ 30 all come out whole. Any other common multiple of 20, 25 and 30 is a multiple of 300.

See Also