LCM for 24, 28 and 42

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
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What's the Least Common Multiple (LCM) of 24, 28 and 42?

Answer

LCM of 24, 28 and 42 is
168

(One hundred sixty-eight)

168 is the smallest positive integer that 24, 28 and 42 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 24, 28 and 42 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 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

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

All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

Prime factor242842Highest power
22322223
33—33
7—777

LCM = 23 × 3 × 7 = 168

Checking the LCM of 24, 28 and 42 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(24, 28) = (24 × 28) ÷ 4 = 672 ÷ 4 = 168

LCM(168, 42) = (168 × 42) ÷ 42 = 7,056 ÷ 42 = 168

LCM(24, 28, 42) = 168

The pairs may be taken in any order — 28 and 42 first, then 24 — and the answer is the same 168. 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 24, 28 and 42? (The answer is: 168). Enter the first number (e.g. '24'), the second (e.g. '28') and the third (e.g. '42'), 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
2427281,512
242828168
2428294,872
242830840
2428315,208
242832672
2428331,848
2428342,856
242835840
242836504
2428376,216
2428383,192
2428392,184
242840840
2428416,888
242842168
2428437,224
2428441,848
2428452,520
2428463,864
2428477,896
242848336
2428491,176
2428504,200
2428512,856
2428522,184
2428538,904
2428541,512
2428559,240
242856168

FAQ

What's the Least Common Multiple (LCM) of 24, 28 and 42?

LCM of 24, 28 and 42 is 168

How to find the LCM of 24, 28 and 42 by prime factorization?

Take every prime that appears in 24, 28 and 42 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 24, 28 and 42 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 24 and 28 is 168, and the LCM of 168 and 42 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 24, 28 and 42?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 24, 168 ÷ 28 and 168 ÷ 42 all come out whole. Any other common multiple of 24, 28 and 42 is a multiple of 168.

See Also