LCM for 25, 45 and 60

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What's the Least Common Multiple (LCM) of 25, 45 and 60?

Answer

LCM of 25, 45 and 60 is
900

First common multiples: 900; 1,800; 2,700; …

900 is divisible by all three: 900 ÷ 25 = 36, 900 ÷ 45 = 20, 900 ÷ 60 = 15 — and 36, 20 and 15 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/25 by 36 and of y/45 by 20 and of z/60 by 15.

25 = 52

45 = 32 × 5

60 = 22 × 3 × 5

Prime254560Highest power
2——2222
3—32332
5525552

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

LCM = 22 × 32 × 52 = 900

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LCM Table

1st2nd3rdLCM
254545225
25454610,350
25454710,575
2545483,600
25454911,025
254550450
2545513,825
25455211,700
25455311,925
2545541,350
2545552,475
25455612,600
2545574,275
25455813,050
25455913,275
254560900
25456113,725
25456213,950
2545631,575
25456414,400
2545652,925
2545664,950
25456715,075
25456815,300
2545695,175
2545703,150
25457115,975
2545721,800
25457316,425
25457416,650

FAQ

What's the Least Common Multiple (LCM) of 25, 45 and 60?

LCM of 25, 45 and 60 is 900

How to find the LCM of 25, 45 and 60 by prime factorization?

Take every prime that appears in 25, 45 and 60 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5² = 900.

Can you get the LCM of 25, 45 and 60 two numbers at a time?

Yes. The LCM of 25 and 45 is 225, and the LCM of 225 and 60 is 900 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 900 divisible by 25, 45 and 60?

Yes, and by definition it is the smallest positive integer that is: 900 ÷ 25, 900 ÷ 45 and 900 ÷ 60 all come out whole. Any other common multiple of 25, 45 and 60 is a multiple of 900.

See Also