LCM for 240, 360 and 900

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

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

Answer

LCM of 240, 360 and 900 is
3,600

(Three thousand six hundred)

3,600 is the smallest positive integer that 240, 360 and 900 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 240, 360 and 900 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 240: 2 × 2 × 2 × 2 × 3 × 5 (exponent form: 24 × 3 × 5)

All Prime Factors of 360: 2 × 2 × 2 × 3 × 3 × 5 (exponent form: 23 × 32 × 5)

All Prime Factors of 900: 2 × 2 × 3 × 3 × 5 × 5 (exponent form: 22 × 32 × 52)

Prime factor240360900Highest power
224232224
33323232
5555252

LCM = 24 × 32 × 52 = 3,600

Checking the LCM of 240, 360 and 900 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(240, 360) = (240 × 360) ÷ 120 = 86,400 ÷ 120 = 720

LCM(720, 900) = (720 × 900) ÷ 180 = 648,000 ÷ 180 = 3,600

LCM(240, 360, 900) = 3,600

The pairs may be taken in any order — 360 and 900 first, then 240 — and the answer is the same 3,600. That is exactly why the two routes on this page agree.

Related Calculations

See Also

About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 240, 360 and 900? (The answer is: 3,600). Enter the first number (e.g. '240'), the second (e.g. '360') and the third (e.g. '900'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
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, and it is the check this page prints. 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