LCM for 7, 8 and 14

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

What's the Least Common Multiple (LCM) of 7, 8 and 14?

Answer

LCM of 7, 8 and 14 is
56

(Fifty-six)

56 is the smallest positive integer that 7, 8 and 14 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 7, 8 and 14 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 14: 2 × 7 (exponent form: 2 × 7)

Prime factor7814Highest power
2—23223
77—77

LCM = 23 × 7 = 56

Checking the LCM of 7, 8 and 14 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, 14) = (56 × 14) ÷ 14 = 784 ÷ 14 = 56

LCM(7, 8, 14) = 56

The pairs may be taken in any order — 8 and 14 first, then 7 — and the answer is the same 56. 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 14? (The answer is: 56). Enter the first number (e.g. '7'), the second (e.g. '8') and the third (e.g. '14'), 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 14?

LCM of 7, 8 and 14 is 56

How to find the LCM of 7, 8 and 14 by prime factorization?

Take every prime that appears in 7, 8 and 14 to the highest power it reaches in any one of them and multiply: 2³ × 7 = 56.

Can you get the LCM of 7, 8 and 14 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 14 is 56 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 56 divisible by 7, 8 and 14?

Yes, and by definition it is the smallest positive integer that is: 56 ÷ 7, 56 ÷ 8 and 56 ÷ 14 all come out whole. Any other common multiple of 7, 8 and 14 is a multiple of 56.

See Also