LCM for 15, 25 and 40

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What's the Least Common Multiple (LCM) of 15, 25 and 40?

Answer

LCM of 15, 25 and 40 is
600

First common multiples: 600; 1,200; 1,800; …

600 is divisible by all three: 600 ÷ 15 = 40, 600 ÷ 25 = 24, 600 ÷ 40 = 15 — and 40, 24 and 15 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/15 by 40 and of y/25 by 24 and of z/40 by 15.

15 = 3 × 5

25 = 52

40 = 23 × 5

Prime152540Highest power
2——2323
33——3
5552552

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

LCM = 23 × 3 × 52 = 600

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LCM Table

1st2nd3rdLCM
15252575
1525261,950
152527675
1525282,100
1525292,175
152530150
1525312,325
1525322,400
152533825
1525342,550
152535525
152536900
1525372,775
1525382,850
152539975
152540600
1525413,075
1525421,050
1525433,225
1525443,300
152545225
1525463,450
1525473,525
1525481,200
1525493,675
152550150
1525511,275
1525523,900
1525533,975
1525541,350

FAQ

What's the Least Common Multiple (LCM) of 15, 25 and 40?

LCM of 15, 25 and 40 is 600

How to find the LCM of 15, 25 and 40 by prime factorization?

Take every prime that appears in 15, 25 and 40 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

Can you get the LCM of 15, 25 and 40 two numbers at a time?

Yes. The LCM of 15 and 25 is 75, and the LCM of 75 and 40 is 600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 600 divisible by 15, 25 and 40?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 15, 600 ÷ 25 and 600 ÷ 40 all come out whole. Any other common multiple of 15, 25 and 40 is a multiple of 600.

See Also