LCM for 7, 10 and 14

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What's the Least Common Multiple (LCM) of 7, 10 and 14?

Answer

LCM of 7, 10 and 14 is
70

First common multiples: 70, 140, 210, …

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

7 — prime

10 = 2 × 5

14 = 2 × 7

Prime71014Highest power
2—222
5—5—5
77—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
171070
271070
3710210
4710140
571070
6710210
771070
7810280
7910630
7101070
71011770
71012420
71013910
7101470
71015210
71016560
710171,190
71018630
710191,330
71020140
71021210
71022770
710231,610
71024840
71025350
71026910
710271,890
71028140
710292,030
71030210

FAQ

What's the Least Common Multiple (LCM) of 7, 10 and 14?

LCM of 7, 10 and 14 is 70

How to find the LCM of 7, 10 and 14 by prime factorization?

Take every prime that appears in 7, 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 7, 10 and 14 two numbers at a time?

Yes. The LCM of 7 and 10 is 70, and the LCM of 70 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 7, 10 and 14?

Yes, and by definition it is the smallest positive integer that is: 70 ÷ 7, 70 ÷ 10 and 70 ÷ 14 all come out whole. Any other common multiple of 7, 10 and 14 is a multiple of 70.

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