LCM for 10, 14 and 20

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What's the Least Common Multiple (LCM) of 10, 14 and 20?

Answer

LCM of 10, 14 and 20 is
140

First common multiples: 140, 280, 420, …

140 is divisible by all three: 140 ÷ 10 = 14, 140 ÷ 14 = 10, 140 ÷ 20 = 7 — and 14, 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/10 by 14 and of y/14 by 10 and of z/20 by 7.

10 = 2 × 5

14 = 2 × 7

20 = 22 × 5

Prime101420Highest power
2222222
55—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 = 22 × 5 × 7 = 140

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LCM Table

1st2nd3rdLCM
5101470
61014210
7101470
81014280
91014630
10101470
101114770
101214420
101314910
10141470
101415210
101416560
1014171,190
101418630
1014191,330
101420140
101421210
101422770
1014231,610
101424840
101425350
101426910
1014271,890
101428140
1014292,030
101430210
1014312,170
1014321,120
1014332,310
1014341,190

FAQ

What's the Least Common Multiple (LCM) of 10, 14 and 20?

LCM of 10, 14 and 20 is 140

How to find the LCM of 10, 14 and 20 by prime factorization?

Take every prime that appears in 10, 14 and 20 to the highest power it reaches in any one of them and multiply: 2² × 5 × 7 = 140.

Can you get the LCM of 10, 14 and 20 two numbers at a time?

Yes. The LCM of 10 and 14 is 70, and the LCM of 70 and 20 is 140 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 140 divisible by 10, 14 and 20?

Yes, and by definition it is the smallest positive integer that is: 140 ÷ 10, 140 ÷ 14 and 140 ÷ 20 all come out whole. Any other common multiple of 10, 14 and 20 is a multiple of 140.

See Also