LCM for 10, 16 and 21

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What's the Least Common Multiple (LCM) of 10, 16 and 21?

Answer

LCM of 10, 16 and 21 is
1,680

First common multiples: 1,680; 3,360; 5,040; …

1,680 is divisible by all three: 1,680 ÷ 10 = 168; 1,680 ÷ 16 = 105; 1,680 ÷ 21 = 80 — and 168, 105 and 80 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 168 and of y/16 by 105 and of z/21 by 80.

10 = 2 × 5

16 = 24

21 = 3 × 7

Prime101621Highest power
2224—24
3——33
55——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 = 24 × 3 × 5 × 7 = 1,680

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LCM Table

1st2nd3rdLCM
61016240
71016560
8101680
91016720
10101680
101116880
101216240
1013161,040
101416560
101516240
10161680
1016171,360
101618720
1016191,520
10162080
1016211,680
101622880
1016231,840
101624240
101625400
1016261,040
1016272,160
101628560
1016292,320
101630240
1016312,480
101632160
1016332,640
1016341,360
101635560

FAQ

What's the Least Common Multiple (LCM) of 10, 16 and 21?

LCM of 10, 16 and 21 is 1,680

How to find the LCM of 10, 16 and 21 by prime factorization?

Take every prime that appears in 10, 16 and 21 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 5 × 7 = 1,680.

Can you get the LCM of 10, 16 and 21 two numbers at a time?

Yes. The LCM of 10 and 16 is 80, and the LCM of 80 and 21 is 1,680 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,680 divisible by 10, 16 and 21?

Yes, and by definition it is the smallest positive integer that is: 1,680 ÷ 10, 1,680 ÷ 16 and 1,680 ÷ 21 all come out whole. Any other common multiple of 10, 16 and 21 is a multiple of 1,680.

See Also