LCM for 8, 21 and 24

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

What's the Least Common Multiple (LCM) of 8, 21 and 24?

Answer

LCM of 8, 21 and 24 is
168

(One hundred sixty-eight)

168 is the smallest positive integer that 8, 21 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 21 and 24 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 21: 3 × 7 (exponent form: 3 × 7)

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

Prime factor82124Highest power
223—2323
3—333
7—7—7

LCM = 23 × 3 × 7 = 168

Checking the LCM of 8, 21 and 24 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, 21) = (8 × 21) ÷ 1 = 168 ÷ 1 = 168

LCM(168, 24) = (168 × 24) ÷ 24 = 4,032 ÷ 24 = 168

LCM(8, 21, 24) = 168

The pairs may be taken in any order — 21 and 24 first, then 8 — 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 8, 21 and 24? (The answer is: 168). Enter the first number (e.g. '8'), the second (e.g. '21') and the third (e.g. '24'), 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
8921504
81021840
811211,848
81221168
813212,184
81421168
81521840
81621336
817212,856
81821504
819213,192
82021840
82121168
821221,848
821233,864
82124168
821254,200
821262,184
821271,512
82128168
821294,872
82130840
821315,208
82132672
821331,848
821342,856
82135840
82136504
821376,216
821383,192

FAQ

What's the Least Common Multiple (LCM) of 8, 21 and 24?

LCM of 8, 21 and 24 is 168

How to find the LCM of 8, 21 and 24 by prime factorization?

Take every prime that appears in 8, 21 and 24 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 8, 21 and 24 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 21 is 168, and the LCM of 168 and 24 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 8, 21 and 24?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 21 and 168 ÷ 24 all come out whole. Any other common multiple of 8, 21 and 24 is a multiple of 168.

See Also