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    LCM for 18, 21 and 36

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

    What's the Least Common Multiple (LCM) of 18, 21 and 36?

    Answer

    LCM of 18, 21 and 36 is
    252

    (Two hundred fifty-two)

    252 is the smallest positive integer that 18, 21 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 18, 21 and 36 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

    All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    Prime factor182136Highest power
    22—2222
    33233232
    7—7—7

    LCM = 22 × 32 × 7 = 252

    Checking the LCM of 18, 21 and 36 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(18, 21) = (18 × 21) ÷ 3 = 378 ÷ 3 = 126

    LCM(126, 36) = (126 × 36) ÷ 18 = 4,536 ÷ 18 = 252

    LCM(18, 21, 36) = 252

    The pairs may be taken in any order — 21 and 36 first, then 18 — and the answer is the same 252. That is exactly why the two routes on this page agree.

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    What is the LCM of 18, 21 and 36?. The LCM of 18, 21 and 36 is 252 — 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
    182121126
    1821221,386
    1821232,898
    182124504
    1821253,150
    1821261,638
    182127378
    182128252
    1821293,654
    182130630
    1821313,906
    1821322,016
    1821331,386
    1821342,142
    182135630
    182136252
    1821374,662
    1821382,394
    1821391,638
    1821402,520
    1821415,166
    182142126
    1821435,418
    1821442,772
    182145630
    1821462,898
    1821475,922
    1821481,008
    182149882
    1821503,150

    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 18, 21 and 36? (The answer is: 252). Enter the first number (e.g. '18'), the second (e.g. '21') and the third (e.g. '36'), 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 18, 21 and 36?

    LCM of 18, 21 and 36 is 252

    How to find the LCM of 18, 21 and 36 by prime factorization?

    Take every prime that appears in 18, 21 and 36 to the highest power it reaches in any one of them and multiply: 2² × 3² × 7 = 252.

    Can you get the LCM of 18, 21 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 18 and 21 is 126, and the LCM of 126 and 36 is 252 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 252 divisible by 18, 21 and 36?

    Yes, and by definition it is the smallest positive integer that is: 252 ÷ 18, 252 ÷ 21 and 252 ÷ 36 all come out whole. Any other common multiple of 18, 21 and 36 is a multiple of 252.

    See Also