LCM for 40, 50 and 80

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

What's the Least Common Multiple (LCM) of 40, 50 and 80?

Answer

LCM of 40, 50 and 80 is
400

(Four hundred)

400 is the smallest positive integer that 40, 50 and 80 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 40, 50 and 80 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 80: 2 × 2 × 2 × 2 × 5 (exponent form: 24 × 5)

Prime factor405080Highest power
22322424
5552552

LCM = 24 × 52 = 400

Checking the LCM of 40, 50 and 80 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(40, 50) = (40 × 50) ÷ 10 = 2,000 ÷ 10 = 200

LCM(200, 80) = (200 × 80) ÷ 40 = 16,000 ÷ 40 = 400

LCM(40, 50, 80) = 400

The pairs may be taken in any order — 50 and 80 first, then 40 — and the answer is the same 400. That is exactly why the two routes on this page agree.

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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 40, 50 and 80? (The answer is: 400). Enter the first number (e.g. '40'), the second (e.g. '50') and the third (e.g. '80'), 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
4050652,600
4050666,600
40506713,400
4050683,400
40506913,800
4050701,400
40507114,200
4050721,800
40507314,600
4050747,400
405075600
4050763,800
40507715,400
4050787,800
40507915,800
405080400
40508116,200
4050828,200
40508316,600
4050844,200
4050853,400
4050868,600
40508717,400
4050882,200
40508917,800
4050901,800
40509118,200
4050924,600
40509318,600
4050949,400

FAQ

What's the Least Common Multiple (LCM) of 40, 50 and 80?

LCM of 40, 50 and 80 is 400

How to find the LCM of 40, 50 and 80 by prime factorization?

Take every prime that appears in 40, 50 and 80 to the highest power it reaches in any one of them and multiply: 2⁴ × 5² = 400.

Can you get the LCM of 40, 50 and 80 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 40 and 50 is 200, and the LCM of 200 and 80 is 400 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 400 divisible by 40, 50 and 80?

Yes, and by definition it is the smallest positive integer that is: 400 ÷ 40, 400 ÷ 50 and 400 ÷ 80 all come out whole. Any other common multiple of 40, 50 and 80 is a multiple of 400.

See Also