LCM for 16, 24 and 28

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 16, 24 and 28?

Answer

LCM of 16, 24 and 28 is
336

(Three hundred thirty-six)

336 is the smallest positive integer that 16, 24 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 16, 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 16: 2 × 2 × 2 × 2 (exponent form: 24)

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 factor162428Highest power
224232224
3—3—3
7——77

LCM = 24 × 3 × 7 = 336

Checking the LCM of 16, 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(16, 24) = (16 × 24) ÷ 8 = 384 ÷ 8 = 48

LCM(48, 28) = (48 × 28) ÷ 4 = 1,344 ÷ 4 = 336

LCM(16, 24, 28) = 336

The pairs may be taken in any order — 24 and 28 first, then 16 — and the answer is the same 336. 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 16, 24 and 28? (The answer is: 336). Enter the first number (e.g. '16'), 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
131624624
141624336
151624240
16162448
161724816
161824144
161924912
162024240
162124336
162224528
1623241,104
16242448
1624251,200
162426624
162427432
162428336
1624291,392
162430240
1624311,488
16243296
162433528
162434816
1624351,680
162436144
1624371,776
162438912
162439624
162440240
1624411,968
162442336

FAQ

What's the Least Common Multiple (LCM) of 16, 24 and 28?

LCM of 16, 24 and 28 is 336

How to find the LCM of 16, 24 and 28 by prime factorization?

Take every prime that appears in 16, 24 and 28 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 × 7 = 336.

Can you get the LCM of 16, 24 and 28 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 16 and 24 is 48, and the LCM of 48 and 28 is 336 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 336 divisible by 16, 24 and 28?

Yes, and by definition it is the smallest positive integer that is: 336 ÷ 16, 336 ÷ 24 and 336 ÷ 28 all come out whole. Any other common multiple of 16, 24 and 28 is a multiple of 336.

See Also