LCM for 24, 36 and 50

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What's the Least Common Multiple (LCM) of 24, 36 and 50?

Answer

LCM of 24, 36 and 50 is
1,800

First common multiples: 1,800; 3,600; 5,400; …

1,800 is divisible by all three: 1,800 ÷ 24 = 75; 1,800 ÷ 36 = 50; 1,800 ÷ 50 = 36 — and 75, 50 and 36 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/24 by 75 and of y/36 by 50 and of z/50 by 36.

24 = 23 × 3

36 = 22 × 32

50 = 2 × 52

Prime243650Highest power
22322223
3332—32
5——5252

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 23 × 32 × 52 = 1,800

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LCM Table

1st2nd3rdLCM
2435362,520
24363672
2436372,664
2436381,368
243639936
243640360
2436412,952
243642504
2436433,096
243644792
243645360
2436461,656
2436473,384
243648144
2436493,528
2436501,800
2436511,224
243652936
2436533,816
243654216
2436553,960
243656504
2436571,368
2436582,088
2436594,248
243660360
2436614,392
2436622,232
243663504
243664576

FAQ

What's the Least Common Multiple (LCM) of 24, 36 and 50?

LCM of 24, 36 and 50 is 1,800

How to find the LCM of 24, 36 and 50 by prime factorization?

Take every prime that appears in 24, 36 and 50 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5² = 1,800.

Can you get the LCM of 24, 36 and 50 two numbers at a time?

Yes. The LCM of 24 and 36 is 72, and the LCM of 72 and 50 is 1,800 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,800 divisible by 24, 36 and 50?

Yes, and by definition it is the smallest positive integer that is: 1,800 ÷ 24, 1,800 ÷ 36 and 1,800 ÷ 50 all come out whole. Any other common multiple of 24, 36 and 50 is a multiple of 1,800.

See Also