LCM for 30, 40 and 50

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What's the Least Common Multiple (LCM) of 30, 40 and 50?

Answer

LCM of 30, 40 and 50 is
600

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

600 is divisible by all three: 600 ÷ 30 = 20, 600 ÷ 40 = 15, 600 ÷ 50 = 12 — and 20, 15 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/30 by 20 and of y/40 by 15 and of z/50 by 12.

30 = 2 × 3 × 5

40 = 23 × 5

50 = 2 × 52

Prime304050Highest power
2223223
33——3
5555252

— = 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
303540840
303640360
3037404,440
3038402,280
3039401,560
304040120
3040414,920
304042840
3040435,160
3040441,320
304045360
3040462,760
3040475,640
304048240
3040495,880
304050600
3040512,040
3040521,560
3040536,360
3040541,080
3040551,320
304056840
3040572,280
3040583,480
3040597,080
304060120
3040617,320
3040623,720
3040632,520
304064960

FAQ

What's the Least Common Multiple (LCM) of 30, 40 and 50?

LCM of 30, 40 and 50 is 600

How to find the LCM of 30, 40 and 50 by prime factorization?

Take every prime that appears in 30, 40 and 50 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² = 600.

Can you get the LCM of 30, 40 and 50 two numbers at a time?

Yes. The LCM of 30 and 40 is 120, and the LCM of 120 and 50 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 30, 40 and 50?

Yes, and by definition it is the smallest positive integer that is: 600 ÷ 30, 600 ÷ 40 and 600 ÷ 50 all come out whole. Any other common multiple of 30, 40 and 50 is a multiple of 600.

See Also