LCM for 45, 135 and 225

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What's the Least Common Multiple (LCM) of 45, 135 and 225?

Answer

LCM of 45, 135 and 225 is
675

First common multiples: 675; 1,350; 2,025; …

675 is divisible by all three: 675 ÷ 45 = 15, 675 ÷ 135 = 5, 675 ÷ 225 = 3 — and 15, 5 and 3 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/45 by 15 and of y/135 by 5 and of z/225 by 3.

45 = 32 × 5

135 = 33 × 5

225 = 32 × 52

Prime45135225Highest power
332333233
5555252

LCM = 33 × 52 = 675

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LCM Table

1st2nd3rdLCM
451352101,890
4513521128,485
4513521228,620
451352139,585
4513521428,890
451352155,805
451352161,080
4513521729,295
4513521829,430
451352199,855
451352205,940
4513522129,835
451352229,990
4513522330,105
4513522430,240
45135225675
4513522630,510
4513522730,645
4513522810,260
4513522930,915
451352306,210
4513523110,395
4513523231,320
4513523331,455
451352343,510
451352356,345
4513523631,860
4513523710,665
4513523832,130
4513523932,265

FAQ

What's the Least Common Multiple (LCM) of 45, 135 and 225?

LCM of 45, 135 and 225 is 675

How to find the LCM of 45, 135 and 225 by prime factorization?

Take every prime that appears in 45, 135 and 225 to the highest power it reaches in any one of them and multiply: 3³ × 5² = 675.

Can you get the LCM of 45, 135 and 225 two numbers at a time?

Yes. The LCM of 45 and 135 is 135, and the LCM of 135 and 225 is 675 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 675 divisible by 45, 135 and 225?

Yes, and by definition it is the smallest positive integer that is: 675 ÷ 45, 675 ÷ 135 and 675 ÷ 225 all come out whole. Any other common multiple of 45, 135 and 225 is a multiple of 675.

See Also