LCM for 7, 8 and 11

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

What's the Least Common Multiple (LCM) of 7, 8 and 11?

Answer

LCM of 7, 8 and 11 is
616

(Six hundred sixteen)

616 is the smallest positive integer that 7, 8 and 11 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 7, 8 and 11 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 7: 7 (exponent form: 7)

All Prime Factors of 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 11: 11 (exponent form: 11)

Prime factor7811Highest power
2—23—23
77——7
11——1111

LCM = 23 × 7 × 11 = 616

Checking the LCM of 7, 8 and 11 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(7, 8) = (7 × 8) ÷ 1 = 56 ÷ 1 = 56

LCM(56, 11) = (56 × 11) ÷ 1 = 616 ÷ 1 = 616

LCM(7, 8, 11) = 616

The pairs may be taken in any order — 8 and 11 first, then 7 — and the answer is the same 616. 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 7, 8 and 11? (The answer is: 616). Enter the first number (e.g. '7'), the second (e.g. '8') and the third (e.g. '11'), 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
17856
27856
378168
47856
578280
678168
77856
78856
789504
7810280
7811616
7812168
7813728
781456
7815840
7816112
7817952
7818504
78191,064
7820280
7821168
7822616
78231,288
7824168
78251,400
7826728
78271,512
782856
78291,624
7830840

FAQ

What's the Least Common Multiple (LCM) of 7, 8 and 11?

LCM of 7, 8 and 11 is 616

How to find the LCM of 7, 8 and 11 by prime factorization?

Take every prime that appears in 7, 8 and 11 to the highest power it reaches in any one of them and multiply: 2³ × 7 × 11 = 616.

Can you get the LCM of 7, 8 and 11 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 7 and 8 is 56, and the LCM of 56 and 11 is 616 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 616 divisible by 7, 8 and 11?

Yes, and by definition it is the smallest positive integer that is: 616 ÷ 7, 616 ÷ 8 and 616 ÷ 11 all come out whole. Any other common multiple of 7, 8 and 11 is a multiple of 616.

See Also