LCM for 9, 10 and 28

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What's the Least Common Multiple (LCM) of 9, 10 and 28?

Answer

LCM of 9, 10 and 28 is
1,260

First common multiples: 1,260; 2,520; 3,780; …

1,260 is divisible by all three: 1,260 ÷ 9 = 140; 1,260 ÷ 10 = 126; 1,260 ÷ 28 = 45 — and 140, 126 and 45 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/9 by 140 and of y/10 by 126 and of z/28 by 45.

9 = 32

10 = 2 × 5

28 = 22 × 7

Prime91028Highest power
2—22222
332——32
5—5—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 = 22 × 32 × 5 × 7 = 1,260

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LCM Table

1st2nd3rdLCM
910131,170
91014630
9101590
91016720
910171,530
9101890
910191,710
91020180
91021630
91022990
910232,070
91024360
91025450
910261,170
91027270
910281,260
910292,610
9103090
910312,790
910321,440
91033990
910341,530
91035630
91036180
910373,330
910381,710
910391,170
91040360
910413,690
91042630

FAQ

What's the Least Common Multiple (LCM) of 9, 10 and 28?

LCM of 9, 10 and 28 is 1,260

How to find the LCM of 9, 10 and 28 by prime factorization?

Take every prime that appears in 9, 10 and 28 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 × 7 = 1,260.

Can you get the LCM of 9, 10 and 28 two numbers at a time?

Yes. The LCM of 9 and 10 is 90, and the LCM of 90 and 28 is 1,260 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,260 divisible by 9, 10 and 28?

Yes, and by definition it is the smallest positive integer that is: 1,260 ÷ 9, 1,260 ÷ 10 and 1,260 ÷ 28 all come out whole. Any other common multiple of 9, 10 and 28 is a multiple of 1,260.

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