LCM for 5, 12 and 25

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What's the Least Common Multiple (LCM) of 5, 12 and 25?

Answer

LCM of 5, 12 and 25 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 5 = 60, 300 ÷ 12 = 25, 300 ÷ 25 = 12 — and 60, 25 and 12 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/5 by 60 and of y/12 by 25 and of z/25 by 12.

5 — prime

12 = 22 × 3

25 = 52

Prime51225Highest power
2—22—22
3—3—3
55—5252

— = 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
5101260
51112660
5121260
51213780
51214420
5121560
51216240
512171,020
51218180
512191,140
5122060
51221420
51222660
512231,380
51224120
51225300
51226780
51227540
51228420
512291,740
5123060
512311,860
51232480
51233660
512341,020
51235420
51236180
512372,220
512381,140
51239780

FAQ

What's the Least Common Multiple (LCM) of 5, 12 and 25?

LCM of 5, 12 and 25 is 300

How to find the LCM of 5, 12 and 25 by prime factorization?

Take every prime that appears in 5, 12 and 25 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 5, 12 and 25 two numbers at a time?

Yes. The LCM of 5 and 12 is 60, and the LCM of 60 and 25 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 5, 12 and 25?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 5, 300 ÷ 12 and 300 ÷ 25 all come out whole. Any other common multiple of 5, 12 and 25 is a multiple of 300.

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