LCM for 15, 30 and 90

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What's the Least Common Multiple (LCM) of 15, 30 and 90?

Answer

LCM of 15, 30 and 90 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 15 = 6, 90 ÷ 30 = 3, 90 ÷ 90 = 1 — and 6, 3 and 1 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/15 by 6 and of y/30 by 3.

15 = 3 × 5

30 = 2 × 3 × 5

90 = 2 × 32 × 5

Prime153090Highest power
2—222
3333232
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
153075150
1530761,140
1530772,310
153078390
1530792,370
153080240
153081810
1530821,230
1530832,490
153084420
153085510
1530861,290
153087870
1530881,320
1530892,670
15309090
1530912,730
1530921,380
153093930
1530941,410
153095570
153096480
1530972,910
1530981,470
153099990
1530100300
15301013,030
1530102510
15301033,090
15301041,560

FAQ

What's the Least Common Multiple (LCM) of 15, 30 and 90?

LCM of 15, 30 and 90 is 90

How to find the LCM of 15, 30 and 90 by prime factorization?

Take every prime that appears in 15, 30 and 90 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 15, 30 and 90 two numbers at a time?

Yes. The LCM of 15 and 30 is 30, and the LCM of 30 and 90 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 15, 30 and 90?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 15, 90 ÷ 30 and 90 ÷ 90 all come out whole. Any other common multiple of 15, 30 and 90 is a multiple of 90.

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