LCM for 4, 21 and 24

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

What's the Least Common Multiple (LCM) of 4, 21 and 24?

Answer

LCM of 4, 21 and 24 is
168

(One hundred sixty-eight)

168 is the smallest positive integer that 4, 21 and 24 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 4, 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 4: 2 × 2 (exponent form: 22)

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 factor42124Highest power
222—2323
3—333
7—7—7

LCM = 23 × 3 × 7 = 168

Checking the LCM of 4, 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(4, 21) = (4 × 21) ÷ 1 = 84 ÷ 1 = 84

LCM(84, 24) = (84 × 24) ÷ 12 = 2,016 ÷ 12 = 168

LCM(4, 21, 24) = 168

The pairs may be taken in any order — 21 and 24 first, then 4 — 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 4, 21 and 24? (The answer is: 168). Enter the first number (e.g. '4'), 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
4921252
41021420
41121924
4122184
413211,092
4142184
41521420
41621336
417211,428
41821252
419211,596
42021420
4212184
42122924
421231,932
42124168
421252,100
421261,092
42127756
4212884
421292,436
42130420
421312,604
42132672
42133924
421341,428
42135420
42136252
421373,108
421381,596

FAQ

What's the Least Common Multiple (LCM) of 4, 21 and 24?

LCM of 4, 21 and 24 is 168

How to find the LCM of 4, 21 and 24 by prime factorization?

Take every prime that appears in 4, 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 4, 21 and 24 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 4 and 21 is 84, and the LCM of 84 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 4, 21 and 24?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 4, 168 ÷ 21 and 168 ÷ 24 all come out whole. Any other common multiple of 4, 21 and 24 is a multiple of 168.

See Also