LCM for 8, 14 and 28

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

What's the Least Common Multiple (LCM) of 8, 14 and 28?

Answer

LCM of 8, 14 and 28 is
56

(Fifty-six)

56 is the smallest positive integer that 8, 14 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 14 and 28 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

Prime factor81428Highest power
22322223
7—777

LCM = 23 × 7 = 56

Checking the LCM of 8, 14 and 28 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(8, 14) = (8 × 14) ÷ 2 = 112 ÷ 2 = 56

LCM(56, 28) = (56 × 28) ÷ 28 = 1,568 ÷ 28 = 56

LCM(8, 14, 28) = 56

The pairs may be taken in any order — 14 and 28 first, then 8 — and the answer is the same 56. 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 8, 14 and 28? (The answer is: 56). Enter the first number (e.g. '8'), the second (e.g. '14') and the third (e.g. '28'), 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
81314728
8141456
81415840
81416112
81417952
81418504
814191,064
81420280
81421168
81422616
814231,288
81424168
814251,400
81426728
814271,512
8142856
814291,624
81430840
814311,736
81432224
814331,848
81434952
81435280
81436504
814372,072
814381,064
814392,184
81440280
814412,296
81442168

FAQ

What's the Least Common Multiple (LCM) of 8, 14 and 28?

LCM of 8, 14 and 28 is 56

How to find the LCM of 8, 14 and 28 by prime factorization?

Take every prime that appears in 8, 14 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 7 = 56.

Can you get the LCM of 8, 14 and 28 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 14 is 56, and the LCM of 56 and 28 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 8, 14 and 28?

Yes, and by definition it is the smallest positive integer that is: 56 ÷ 8, 56 ÷ 14 and 56 ÷ 28 all come out whole. Any other common multiple of 8, 14 and 28 is a multiple of 56.

See Also