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    LCM for 28, 42 and 105

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

    What's the Least Common Multiple (LCM) of 28, 42 and 105?

    Answer

    LCM of 28, 42 and 105 is
    420

    (Four hundred twenty)

    420 is the smallest positive integer that 28, 42 and 105 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 28, 42 and 105 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

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

    All Prime Factors of 105: 3 × 5 × 7 (exponent form: 3 × 5 × 7)

    Prime factor2842105Highest power
    2222—22
    3—333
    5——55
    77777

    LCM = 22 × 3 × 5 × 7 = 420

    Checking the LCM of 28, 42 and 105 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(28, 42) = (28 × 42) ÷ 14 = 1,176 ÷ 14 = 84

    LCM(84, 105) = (84 × 105) ÷ 21 = 8,820 ÷ 21 = 420

    LCM(28, 42, 105) = 420

    The pairs may be taken in any order — 42 and 105 first, then 28 — and the answer is the same 420. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 28, 42 and 105?. The LCM of 28, 42 and 105 is 420 — 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
    2842901,260
    2842911,092
    2842921,932
    2842932,604
    2842943,948
    2842957,980
    284296672
    2842978,148
    284298588
    2842992,772
    28421002,100
    28421018,484
    28421021,428
    28421038,652
    28421042,184
    2842105420
    28421064,452
    28421078,988
    2842108756
    28421099,156
    28421104,620
    28421113,108
    2842112336
    28421139,492
    28421141,596
    28421159,660
    28421162,436
    28421173,276
    28421184,956
    28421191,428

    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 28, 42 and 105? (The answer is: 420). Enter the first number (e.g. '28'), the second (e.g. '42') and the third (e.g. '105'), 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 28, 42 and 105?

    LCM of 28, 42 and 105 is 420

    How to find the LCM of 28, 42 and 105 by prime factorization?

    Take every prime that appears in 28, 42 and 105 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 7 = 420.

    Can you get the LCM of 28, 42 and 105 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 28 and 42 is 84, and the LCM of 84 and 105 is 420 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 420 divisible by 28, 42 and 105?

    Yes, and by definition it is the smallest positive integer that is: 420 ÷ 28, 420 ÷ 42 and 420 ÷ 105 all come out whole. Any other common multiple of 28, 42 and 105 is a multiple of 420.

    See Also