LCM for 280, 360 and 840

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

What's the Least Common Multiple (LCM) of 280, 360 and 840?

Answer

LCM of 280, 360 and 840 is
2,520

(Two thousand five hundred twenty)

2,520 is the smallest positive integer that 280, 360 and 840 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 280, 360 and 840 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 280: 2 × 2 × 2 × 5 × 7 (exponent form: 23 × 5 × 7)

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

All Prime Factors of 840: 2 × 2 × 2 × 3 × 5 × 7 (exponent form: 23 × 3 × 5 × 7)

Prime factor280360840Highest power
223232323
3—32332
55555
77—77

LCM = 23 × 32 × 5 × 7 = 2,520

Checking the LCM of 280, 360 and 840 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(280, 360) = (280 × 360) ÷ 40 = 100,800 ÷ 40 = 2,520

LCM(2,520, 840) = (2,520 × 840) ÷ 840 = 2,116,800 ÷ 840 = 2,520

LCM(280, 360, 840) = 2,520

The pairs may be taken in any order — 360 and 840 first, then 280 — and the answer is the same 2,520. 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 280, 360 and 840? (The answer is: 2,520). Enter the first number (e.g. '280'), the second (e.g. '360') and the third (e.g. '840'), 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
280360825138,600
280360826148,680
2803608272,084,040
28036082857,960
2803608292,089,080
280360830209,160
280360831698,040
280360832262,080
280360833299,880
280360834350,280
280360835420,840
280360836526,680
280360837234,360
2803608381,055,880
2803608392,114,280
2803608402,520
2803608412,119,320
2803608421,060,920
280360843708,120
280360844531,720
280360845425,880
280360846118,440
280360847304,920
280360848267,120
280360849713,160
280360850214,200
2803608512,144,520
280360852178,920
2803608532,149,560
280360854153,720

FAQ

What's the Least Common Multiple (LCM) of 280, 360 and 840?

LCM of 280, 360 and 840 is 2,520

How to find the LCM of 280, 360 and 840 by prime factorization?

Take every prime that appears in 280, 360 and 840 to the highest power it reaches in any one of them and multiply: 2³ × 3² × 5 × 7 = 2,520.

Can you get the LCM of 280, 360 and 840 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 280 and 360 is 2,520, and the LCM of 2,520 and 840 is 2,520 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 2,520 divisible by 280, 360 and 840?

Yes, and by definition it is the smallest positive integer that is: 2,520 ÷ 280, 2,520 ÷ 360 and 2,520 ÷ 840 all come out whole. Any other common multiple of 280, 360 and 840 is a multiple of 2,520.

See Also