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    LCM for 24, 28 and 42

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

    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

    See Also

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    What is the LCM of 24, 28 and 42?. The LCM of 24, 28 and 42 is 168 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
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    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

    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

    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