LCM for 12, 30 and 50

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What's the Least Common Multiple (LCM) of 12, 30 and 50?

Answer

LCM of 12, 30 and 50 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 12 = 25, 300 ÷ 30 = 10, 300 ÷ 50 = 6 — and 25, 10 and 6 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/12 by 25 and of y/30 by 10 and of z/50 by 6.

12 = 22 × 3

30 = 2 × 3 × 5

50 = 2 × 52

Prime123050Highest power
2222222
333—3
5—55252

— = 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
123035420
123036180
1230372,220
1230381,140
123039780
123040120
1230412,460
123042420
1230432,580
123044660
123045180
1230461,380
1230472,820
123048240
1230492,940
123050300
1230511,020
123052780
1230533,180
123054540
123055660
123056840
1230571,140
1230581,740
1230593,540
12306060
1230613,660
1230621,860
1230631,260
123064960

FAQ

What's the Least Common Multiple (LCM) of 12, 30 and 50?

LCM of 12, 30 and 50 is 300

How to find the LCM of 12, 30 and 50 by prime factorization?

Take every prime that appears in 12, 30 and 50 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 12, 30 and 50 two numbers at a time?

Yes. The LCM of 12 and 30 is 60, and the LCM of 60 and 50 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 12, 30 and 50?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 12, 300 ÷ 30 and 300 ÷ 50 all come out whole. Any other common multiple of 12, 30 and 50 is a multiple of 300.

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