LCM for 10, 15 and 45

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What's the Least Common Multiple (LCM) of 10, 15 and 45?

Answer

LCM of 10, 15 and 45 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 10 = 9, 90 ÷ 15 = 6, 90 ÷ 45 = 2 — and 9, 6 and 2 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 9 and of y/15 by 6 and of z/45 by 2.

10 = 2 × 5

15 = 3 × 5

45 = 32 × 5

Prime101545Highest power
22——2
3—33232
55555

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2 × 32 × 5 = 90

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LCM Table

1st2nd3rdLCM
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
101550150
101551510
101552780
1015531,590
101554270
101555330
101556840
101557570
101558870
1015591,770

FAQ

What's the Least Common Multiple (LCM) of 10, 15 and 45?

LCM of 10, 15 and 45 is 90

How to find the LCM of 10, 15 and 45 by prime factorization?

Take every prime that appears in 10, 15 and 45 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 10, 15 and 45 two numbers at a time?

Yes. The LCM of 10 and 15 is 30, and the LCM of 30 and 45 is 90 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 90 divisible by 10, 15 and 45?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 10, 90 ÷ 15 and 90 ÷ 45 all come out whole. Any other common multiple of 10, 15 and 45 is a multiple of 90.

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