LCM for 2, 5 and 9

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What's the Least Common Multiple (LCM) of 2, 5 and 9?

Answer

LCM of 2, 5 and 9 is
90

First common multiples: 90, 180, 270, …

90 is divisible by all three: 90 ÷ 2 = 45, 90 ÷ 5 = 18, 90 ÷ 9 = 10 — and 45, 18 and 10 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/2 by 45 and of y/5 by 18 and of z/9 by 10.

2 — prime

5 — prime

9 = 32

Prime259Highest power
22——2
3——3232
5—5—5

— = 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
12510
22510
23530
24520
25510
25630
25770
25840
25990
251010
2511110
251260
2513130
251470
251530
251680
2517170
251890
2519190
252020
2521210
2522110
2523230
2524120
252550
2526130
2527270
2528140
2529290
253030

FAQ

What's the Least Common Multiple (LCM) of 2, 5 and 9?

LCM of 2, 5 and 9 is 90

How to find the LCM of 2, 5 and 9 by prime factorization?

Take every prime that appears in 2, 5 and 9 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 = 90.

Can you get the LCM of 2, 5 and 9 two numbers at a time?

Yes. The LCM of 2 and 5 is 10, and the LCM of 10 and 9 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 2, 5 and 9?

Yes, and by definition it is the smallest positive integer that is: 90 ÷ 2, 90 ÷ 5 and 90 ÷ 9 all come out whole. Any other common multiple of 2, 5 and 9 is a multiple of 90.

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