LCM for 5, 10 and 14

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What's the Least Common Multiple (LCM) of 5, 10 and 14?

Answer

LCM of 5, 10 and 14 is
70

First common multiples: 70, 140, 210, …

70 is divisible by all three: 70 ÷ 5 = 14, 70 ÷ 10 = 7, 70 ÷ 14 = 5 — and 14, 7 and 5 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/5 by 14 and of y/10 by 7 and of z/14 by 5.

5 — prime

10 = 2 × 5

14 = 2 × 7

Prime51014Highest power
2—222
555—5
7——77

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

LCM = 2 × 5 × 7 = 70

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LCM Table

1st2nd3rdLCM
151010
251010
351030
451020
551010
561030
571070
581040
591090
5101010
51011110
5101260
51013130
5101470
5101530
5101680
51017170
5101890
51019190
5102020
51021210
51022110
51023230
51024120
5102550
51026130
51027270
51028140
51029290
5103030

FAQ

What's the Least Common Multiple (LCM) of 5, 10 and 14?

LCM of 5, 10 and 14 is 70

How to find the LCM of 5, 10 and 14 by prime factorization?

Take every prime that appears in 5, 10 and 14 to the highest power it reaches in any one of them and multiply: 2 × 5 × 7 = 70.

Can you get the LCM of 5, 10 and 14 two numbers at a time?

Yes. The LCM of 5 and 10 is 10, and the LCM of 10 and 14 is 70 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 70 divisible by 5, 10 and 14?

Yes, and by definition it is the smallest positive integer that is: 70 ÷ 5, 70 ÷ 10 and 70 ÷ 14 all come out whole. Any other common multiple of 5, 10 and 14 is a multiple of 70.

See Also