LCM for 10, 25 and 30

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What's the Least Common Multiple (LCM) of 10, 25 and 30?

Answer

LCM of 10, 25 and 30 is
150

First common multiples: 150, 300, 450, …

150 is divisible by all three: 150 ÷ 10 = 15, 150 ÷ 25 = 6, 150 ÷ 30 = 5 — and 15, 6 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/10 by 15 and of y/25 by 6 and of z/30 by 5.

10 = 2 × 5

25 = 52

30 = 2 × 3 × 5

Prime102530Highest power
22—22
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 = 2 × 3 × 52 = 150

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LCM Table

1st2nd3rdLCM
101525150
101625400
101725850
101825450
101925950
102025100
1021251,050
102225550
1023251,150
102425600
10252550
102526650
1025271,350
102528700
1025291,450
102530150
1025311,550
102532800
1025331,650
102534850
102535350
102536900
1025371,850
102538950
1025391,950
102540200
1025412,050
1025421,050
1025432,150
1025441,100

FAQ

What's the Least Common Multiple (LCM) of 10, 25 and 30?

LCM of 10, 25 and 30 is 150

How to find the LCM of 10, 25 and 30 by prime factorization?

Take every prime that appears in 10, 25 and 30 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5² = 150.

Can you get the LCM of 10, 25 and 30 two numbers at a time?

Yes. The LCM of 10 and 25 is 50, and the LCM of 50 and 30 is 150 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 150 divisible by 10, 25 and 30?

Yes, and by definition it is the smallest positive integer that is: 150 ÷ 10, 150 ÷ 25 and 150 ÷ 30 all come out whole. Any other common multiple of 10, 25 and 30 is a multiple of 150.

See Also