LCM for 25, 30 and 40

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What's the Least Common Multiple (LCM) of 25, 30 and 40?

Answer

LCM of 25, 30 and 40 is
600

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

600 is divisible by all three: 600 ÷ 25 = 24, 600 ÷ 30 = 20, 600 ÷ 40 = 15 — and 24, 20 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/25 by 24 and of y/30 by 20 and of z/40 by 15.

25 = 52

30 = 2 × 3 × 5

40 = 23 × 5

Prime253040Highest power
2—22323
3—3—3
5525552

— = 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
252530150
2526301,950
2527301,350
2528302,100
2529304,350
253030150
2530314,650
2530322,400
2530331,650
2530342,550
2530351,050
253036900
2530375,550
2530382,850
2530391,950
253040600
2530416,150
2530421,050
2530436,450
2530443,300
253045450
2530463,450
2530477,050
2530481,200
2530497,350
253050150
2530512,550
2530523,900
2530537,950
2530541,350

FAQ

What's the Least Common Multiple (LCM) of 25, 30 and 40?

LCM of 25, 30 and 40 is 600

How to find the LCM of 25, 30 and 40 by prime factorization?

Take every prime that appears in 25, 30 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 25, 30 and 40 two numbers at a time?

Yes. The LCM of 25 and 30 is 150, and the LCM of 150 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 25, 30 and 40?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 25, 600 ÷ 30 and 600 ÷ 40 all come out whole. Any other common multiple of 25, 30 and 40 is a multiple of 600.

See Also