LCM for 35, 40 and 120

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

What's the Least Common Multiple (LCM) of 35, 40 and 120?

Answer

LCM of 35, 40 and 120 is
840

(Eight hundred forty)

840 is the smallest positive integer that 35, 40 and 120 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 35, 40 and 120 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 35: 5 × 7 (exponent form: 5 × 7)

All Prime Factors of 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

All Prime Factors of 120: 2 × 2 × 2 × 3 × 5 (exponent form: 23 × 3 × 5)

Prime factor3540120Highest power
2—232323
3——33
55555
77——7

LCM = 23 × 3 × 5 × 7 = 840

Checking the LCM of 35, 40 and 120 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(35, 40) = (35 × 40) ÷ 5 = 1,400 ÷ 5 = 280

LCM(280, 120) = (280 × 120) ÷ 40 = 33,600 ÷ 40 = 840

LCM(35, 40, 120) = 840

The pairs may be taken in any order — 40 and 120 first, then 35 — and the answer is the same 840. That is exactly why the two routes on this page agree.

Related Calculations

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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 35, 40 and 120? (The answer is: 840). Enter the first number (e.g. '35'), the second (e.g. '40') and the third (e.g. '120'), 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
3540105840
354010614,840
354010729,960
35401087,560
354010930,520
35401103,080
354011131,080
3540112560
354011331,640
354011415,960
35401156,440
35401168,120
354011732,760
354011816,520
35401194,760
3540120840
354012133,880
354012217,080
354012334,440
35401248,680
35401257,000
35401262,520
354012735,560
35401284,480
354012936,120
35401303,640
354013136,680
35401329,240
35401335,320
354013418,760

FAQ

What's the Least Common Multiple (LCM) of 35, 40 and 120?

LCM of 35, 40 and 120 is 840

How to find the LCM of 35, 40 and 120 by prime factorization?

Take every prime that appears in 35, 40 and 120 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

Can you get the LCM of 35, 40 and 120 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 35 and 40 is 280, and the LCM of 280 and 120 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 840 divisible by 35, 40 and 120?

Yes, and by definition it is the smallest positive integer that is: 840 ÷ 35, 840 ÷ 40 and 840 ÷ 120 all come out whole. Any other common multiple of 35, 40 and 120 is a multiple of 840.

See Also