LCM for 50, 100 and 150

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What's the Least Common Multiple (LCM) of 50, 100 and 150?

Answer

LCM of 50, 100 and 150 is
300

First common multiples: 300, 600, 900, …

300 is divisible by all three: 300 ÷ 50 = 6, 300 ÷ 100 = 3, 300 ÷ 150 = 2 — and 6, 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 6 and of y/100 by 3 and of z/150 by 2.

50 = 2 × 52

100 = 22 × 52

150 = 2 × 3 × 52

Prime50100150Highest power
2222222
3——33
552525252

— = 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
501001352,700
501001363,400
5010013713,700
501001386,900
5010013913,900
50100140700
5010014114,100
501001427,100
5010014314,300
501001443,600
501001452,900
501001467,300
5010014714,700
501001483,700
5010014914,900
50100150300
5010015115,100
501001523,800
5010015315,300
501001547,700
501001553,100
501001563,900
5010015715,700
501001587,900
5010015915,900
50100160800
5010016116,100
501001628,100
5010016316,300
501001644,100

FAQ

What's the Least Common Multiple (LCM) of 50, 100 and 150?

LCM of 50, 100 and 150 is 300

How to find the LCM of 50, 100 and 150 by prime factorization?

Take every prime that appears in 50, 100 and 150 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5² = 300.

Can you get the LCM of 50, 100 and 150 two numbers at a time?

Yes. The LCM of 50 and 100 is 100, and the LCM of 100 and 150 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 50, 100 and 150?

Yes, and by definition it is the smallest positive integer that is: 300 ÷ 50, 300 ÷ 100 and 300 ÷ 150 all come out whole. Any other common multiple of 50, 100 and 150 is a multiple of 300.

See Also