LCM for 8, 42 and 84

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What's the Least Common Multiple (LCM) of 8, 42 and 84?

Answer

LCM of 8, 42 and 84 is
168

First common multiples: 168, 336, 504, …

168 is divisible by all three: 168 ÷ 8 = 21, 168 ÷ 42 = 4, 168 ÷ 84 = 2 — and 21, 4 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/8 by 21 and of y/42 by 4 and of z/84 by 2.

8 = 23

42 = 2 × 3 × 7

84 = 22 × 3 × 7

Prime84284Highest power
22322223
3—333
7—777

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

LCM = 23 × 3 × 7 = 168

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LCM Table

1st2nd3rdLCM
842693,864
84270840
8427111,928
84272504
8427312,264
842746,216
842754,200
842763,192
842771,848
842782,184
8427913,272
842801,680
842814,536
842826,888
8428313,944
84284168
8428514,280
842867,224
842874,872
842881,848
8428914,952
842902,520
842912,184
842923,864
842935,208
842947,896
8429515,960
84296672
8429716,296
842981,176

FAQ

What's the Least Common Multiple (LCM) of 8, 42 and 84?

LCM of 8, 42 and 84 is 168

How to find the LCM of 8, 42 and 84 by prime factorization?

Take every prime that appears in 8, 42 and 84 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 8, 42 and 84 two numbers at a time?

Yes. The LCM of 8 and 42 is 168, and the LCM of 168 and 84 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 8, 42 and 84?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 42 and 168 ÷ 84 all come out whole. Any other common multiple of 8, 42 and 84 is a multiple of 168.

See Also