LCM for 2, 7 and 10

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 2, 7 and 10?

Answer

LCM of 2, 7 and 10 is
70

First common multiples: 70, 140, 210, …

70 is divisible by all three: 70 ÷ 2 = 35, 70 ÷ 7 = 10, 70 ÷ 10 = 7 — and 35, 10 and 7 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/2 by 35 and of y/7 by 10 and of z/10 by 7.

2 — prime

7 — prime

10 = 2 × 5

Prime2710Highest power
22—22
5——55
7—7—7

— = 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
12714
22714
23742
24728
25770
26742
27714
27856
279126
271070
2711154
271284
2713182
271414
2715210
2716112
2717238
2718126
2719266
2720140
272142
2722154
2723322
2724168
2725350
2726182
2727378
272828
2729406
2730210

FAQ

What's the Least Common Multiple (LCM) of 2, 7 and 10?

LCM of 2, 7 and 10 is 70

How to find the LCM of 2, 7 and 10 by prime factorization?

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

Can you get the LCM of 2, 7 and 10 two numbers at a time?

Yes. The LCM of 2 and 7 is 14, and the LCM of 14 and 10 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 2, 7 and 10?

Yes, and by definition it is the smallest positive integer that is: 70 ÷ 2, 70 ÷ 7 and 70 ÷ 10 all come out whole. Any other common multiple of 2, 7 and 10 is a multiple of 70.

See Also