LCM for 240, 360 and 900

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What's the Least Common Multiple (LCM) of 240, 360 and 900?

Answer

LCM of 240, 360 and 900 is
3,600

First common multiples: 3,600; 7,200; 10,800; …

3,600 is divisible by all three: 3,600 ÷ 240 = 15; 3,600 ÷ 360 = 10; 3,600 ÷ 900 = 4 — and 15, 10 and 4 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/240 by 15 and of y/360 by 10 and of z/900 by 4.

240 = 24 × 3 × 5

360 = 23 × 32 × 5

900 = 22 × 32 × 52

Prime240360900Highest power
224232224
33323232
5555252

LCM = 24 × 32 × 52 = 3,600

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See Also

LCM Table

1st2nd3rdLCM
24036088542,480
240360886318,960
240360887638,640
24036088826,640
240360889640,080
24036089064,080
24036089171,280
240360892160,560
240360893642,960
240360894107,280
240360895128,880
24036089640,320
240360897215,280
240360898323,280
240360899647,280
2403609003,600
240360901648,720
240360902324,720
240360903216,720
24036090481,360
240360905130,320
240360906108,720
240360907653,040
240360908163,440
24036090972,720
24036091065,520
240360911655,920
24036091213,680
240360913657,360
240360914329,040

FAQ

What's the Least Common Multiple (LCM) of 240, 360 and 900?

LCM of 240, 360 and 900 is 3,600

How to find the LCM of 240, 360 and 900 by prime factorization?

Take every prime that appears in 240, 360 and 900 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5² = 3,600.

Can you get the LCM of 240, 360 and 900 two numbers at a time?

Yes. The LCM of 240 and 360 is 720, and the LCM of 720 and 900 is 3,600 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 3,600 divisible by 240, 360 and 900?

Yes, and by definition it is the smallest positive integer that is: 3,600 ÷ 240, 3,600 ÷ 360 and 3,600 ÷ 900 all come out whole. Any other common multiple of 240, 360 and 900 is a multiple of 3,600.

See Also