LCM for 10, 50 and 80

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

What's the Least Common Multiple (LCM) of 10, 50 and 80?

Answer

LCM of 10, 50 and 80 is
400

(Four hundred)

400 is the smallest positive integer that 10, 50 and 80 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 10, 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 10: 2 × 5 (exponent form: 2 × 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 factor105080Highest power
2222424
5552552

LCM = 24 × 52 = 400

Checking the LCM of 10, 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(10, 50) = (10 × 50) ÷ 10 = 500 ÷ 10 = 50

LCM(50, 80) = (50 × 80) ÷ 10 = 4,000 ÷ 10 = 400

LCM(10, 50, 80) = 400

The pairs may be taken in any order — 50 and 80 first, then 10 — 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 10, 50 and 80? (The answer is: 400). Enter the first number (e.g. '10'), 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
105065650
1050661,650
1050673,350
1050681,700
1050693,450
105070350
1050713,550
1050721,800
1050733,650
1050741,850
105075150
1050761,900
1050773,850
1050781,950
1050793,950
105080400
1050814,050
1050822,050
1050834,150
1050842,100
105085850
1050862,150
1050874,350
1050882,200
1050894,450
105090450
1050914,550
1050922,300
1050934,650
1050942,350

FAQ

What's the Least Common Multiple (LCM) of 10, 50 and 80?

LCM of 10, 50 and 80 is 400

How to find the LCM of 10, 50 and 80 by prime factorization?

Take every prime that appears in 10, 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 10, 50 and 80 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 10 and 50 is 50, and the LCM of 50 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 10, 50 and 80?

Yes, and by definition it is the smallest positive integer that is: 400 ÷ 10, 400 ÷ 50 and 400 ÷ 80 all come out whole. Any other common multiple of 10, 50 and 80 is a multiple of 400.

See Also