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    LCM for 4, 16 and 36

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

    What's the Least Common Multiple (LCM) of 4, 16 and 36?

    Answer

    LCM of 4, 16 and 36 is
    144

    (One hundred forty-four)

    144 is the smallest positive integer that 4, 16 and 36 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 16 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 4: 2 × 2 (exponent form: 22)

    All Prime Factors of 16: 2 × 2 × 2 × 2 (exponent form: 24)

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

    Prime factor41636Highest power
    222242224
    3——3232

    LCM = 24 × 32 = 144

    Checking the LCM of 4, 16 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(4, 16) = (4 × 16) ÷ 4 = 64 ÷ 4 = 16

    LCM(16, 36) = (16 × 36) ÷ 4 = 576 ÷ 4 = 144

    LCM(4, 16, 36) = 144

    The pairs may be taken in any order — 16 and 36 first, then 4 — and the answer is the same 144. That is exactly why the two routes on this page agree.

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    What is the LCM of 4, 16 and 36?. The LCM of 4, 16 and 36 is 144 — 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
    41621336
    41622176
    41623368
    4162448
    41625400
    41626208
    41627432
    41628112
    41629464
    41630240
    41631496
    4163232
    41633528
    41634272
    41635560
    41636144
    41637592
    41638304
    41639624
    4164080
    41641656
    41642336
    41643688
    41644176
    41645720
    41646368
    41647752
    4164848
    41649784
    41650400

    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, 16 and 36? (The answer is: 144). Enter the first number (e.g. '4'), the second (e.g. '16') 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 4, 16 and 36?

    LCM of 4, 16 and 36 is 144

    How to find the LCM of 4, 16 and 36 by prime factorization?

    Take every prime that appears in 4, 16 and 36 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² = 144.

    Can you get the LCM of 4, 16 and 36 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 16 is 16, and the LCM of 16 and 36 is 144 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 144 divisible by 4, 16 and 36?

    Yes, and by definition it is the smallest positive integer that is: 144 ÷ 4, 144 ÷ 16 and 144 ÷ 36 all come out whole. Any other common multiple of 4, 16 and 36 is a multiple of 144.

    See Also