LCM for 14, 24 and 28

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 14, 24 and 28?

Answer

LCM of 14, 24 and 28 is
168

(One hundred sixty-eight)

168 is the smallest positive integer that 14, 24 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 14, 24 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 14: 2 × 7 (exponent form: 2 × 7)

All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

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

Prime factor142428Highest power
22232223
3—3—3
77—77

LCM = 23 × 3 × 7 = 168

Checking the LCM of 14, 24 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(14, 24) = (14 × 24) ÷ 2 = 336 ÷ 2 = 168

LCM(168, 28) = (168 × 28) ÷ 28 = 4,704 ÷ 28 = 168

LCM(14, 24, 28) = 168

The pairs may be taken in any order — 24 and 28 first, then 14 — and the answer is the same 168. 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 14, 24 and 28? (The answer is: 168). Enter the first number (e.g. '14'), the second (e.g. '24') 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
1314242,184
141424168
141524840
141624336
1417242,856
141824504
1419243,192
142024840
142124168
1422241,848
1423243,864
142424168
1424254,200
1424262,184
1424271,512
142428168
1424294,872
142430840
1424315,208
142432672
1424331,848
1424342,856
142435840
142436504
1424376,216
1424383,192
1424392,184
142440840
1424416,888
142442168

FAQ

What's the Least Common Multiple (LCM) of 14, 24 and 28?

LCM of 14, 24 and 28 is 168

How to find the LCM of 14, 24 and 28 by prime factorization?

Take every prime that appears in 14, 24 and 28 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 14, 24 and 28 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 14 and 24 is 168, and the LCM of 168 and 28 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 14, 24 and 28?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 14, 168 ÷ 24 and 168 ÷ 28 all come out whole. Any other common multiple of 14, 24 and 28 is a multiple of 168.

See Also