LCM for 50, 150 and 225

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What's the Least Common Multiple (LCM) of 50, 150 and 225?

Answer

LCM of 50, 150 and 225 is
450

First common multiples: 450; 900; 1,350; …

450 is divisible by all three: 450 ÷ 50 = 9, 450 ÷ 150 = 3, 450 ÷ 225 = 2 — and 9, 3 and 2 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/50 by 9 and of y/150 by 3 and of z/225 by 2.

50 = 2 × 52

150 = 2 × 3 × 52

225 = 32 × 52

Prime50150225Highest power
222—2
3—33232
552525252

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

LCM = 2 × 32 × 52 = 450

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LCM Table

1st2nd3rdLCM
501502101,050
5015021131,650
5015021215,900
5015021310,650
5015021416,050
501502156,450
501502165,400
5015021732,550
5015021816,350
5015021910,950
501502203,300
5015022133,150
501502225,550
5015022333,450
5015022416,800
50150225450
5015022616,950
5015022734,050
501502285,700
5015022934,350
501502303,450
5015023111,550
5015023217,400
5015023334,950
501502345,850
501502357,050
5015023617,700
5015023711,850
5015023817,850
5015023935,850

FAQ

What's the Least Common Multiple (LCM) of 50, 150 and 225?

LCM of 50, 150 and 225 is 450

How to find the LCM of 50, 150 and 225 by prime factorization?

Take every prime that appears in 50, 150 and 225 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5² = 450.

Can you get the LCM of 50, 150 and 225 two numbers at a time?

Yes. The LCM of 50 and 150 is 150, and the LCM of 150 and 225 is 450 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 450 divisible by 50, 150 and 225?

Yes, and by definition it is the smallest positive integer that is: 450 ÷ 50, 450 ÷ 150 and 450 ÷ 225 all come out whole. Any other common multiple of 50, 150 and 225 is a multiple of 450.

See Also