LCM for 10, 15 and 35

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What's the Least Common Multiple (LCM) of 10, 15 and 35?

Answer

LCM of 10, 15 and 35 is
210

First common multiples: 210, 420, 630, …

210 is divisible by all three: 210 ÷ 10 = 21, 210 ÷ 15 = 14, 210 ÷ 35 = 6 — and 21, 14 and 6 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 21 and of y/15 by 14 and of z/35 by 6.

10 = 2 × 5

15 = 3 × 5

35 = 5 × 7

Prime101535Highest power
22——2
3—3—3
55555
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 × 3 × 5 × 7 = 210

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LCM Table

1st2nd3rdLCM
10152060
101521210
101522330
101523690
101524120
101525150
101526390
101527270
101528420
101529870
10153030
101531930
101532480
101533330
101534510
101535210
101536180
1015371,110
101538570
101539390
101540120
1015411,230
101542210
1015431,290
101544660
10154590
101546690
1015471,410
101548240
1015491,470

FAQ

What's the Least Common Multiple (LCM) of 10, 15 and 35?

LCM of 10, 15 and 35 is 210

How to find the LCM of 10, 15 and 35 by prime factorization?

Take every prime that appears in 10, 15 and 35 to the highest power it reaches in any one of them and multiply: 2 × 3 × 5 × 7 = 210.

Can you get the LCM of 10, 15 and 35 two numbers at a time?

Yes. The LCM of 10 and 15 is 30, and the LCM of 30 and 35 is 210 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 210 divisible by 10, 15 and 35?

Yes, and by definition it is the smallest positive integer that is: 210 ÷ 10, 210 ÷ 15 and 210 ÷ 35 all come out whole. Any other common multiple of 10, 15 and 35 is a multiple of 210.

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