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    LCM for 66, 99 and 132

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

    What's the Least Common Multiple (LCM) of 66, 99 and 132?

    Answer

    LCM of 66, 99 and 132 is
    396

    (Three hundred ninety-six)

    396 is the smallest positive integer that 66, 99 and 132 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 66, 99 and 132 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 66: 2 × 3 × 11 (exponent form: 2 × 3 × 11)

    All Prime Factors of 99: 3 × 3 × 11 (exponent form: 32 × 11)

    All Prime Factors of 132: 2 × 2 × 3 × 11 (exponent form: 22 × 3 × 11)

    Prime factor6699132Highest power
    22—2222
    3332332
    1111111111

    LCM = 22 × 32 × 11 = 396

    Checking the LCM of 66, 99 and 132 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(66, 99) = (66 × 99) ÷ 33 = 6,534 ÷ 33 = 198

    LCM(198, 132) = (198 × 132) ÷ 66 = 26,136 ÷ 66 = 396

    LCM(66, 99, 132) = 396

    The pairs may be taken in any order — 99 and 132 first, then 66 — and the answer is the same 396. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 66, 99 and 132?. The LCM of 66, 99 and 132 is 396 — 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
    66991172,574
    669911811,682
    669911923,562
    66991203,960
    66991212,178
    669912212,078
    66991238,118
    669912412,276
    669912524,750
    66991261,386
    669912725,146
    669912812,672
    66991298,514
    669913012,870
    669913125,938
    6699132396
    669913326,334
    669913413,266
    66991352,970
    669913613,464
    669913727,126
    66991384,554
    669913927,522
    669914013,860
    66991419,306
    669914214,058
    66991432,574
    66991441,584
    669914528,710
    669914614,454

    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 66, 99 and 132? (The answer is: 396). Enter the first number (e.g. '66'), the second (e.g. '99') and the third (e.g. '132'), 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 66, 99 and 132?

    LCM of 66, 99 and 132 is 396

    How to find the LCM of 66, 99 and 132 by prime factorization?

    Take every prime that appears in 66, 99 and 132 to the highest power it reaches in any one of them and multiply: 2² × 3² × 11 = 396.

    Can you get the LCM of 66, 99 and 132 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 66 and 99 is 198, and the LCM of 198 and 132 is 396 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 396 divisible by 66, 99 and 132?

    Yes, and by definition it is the smallest positive integer that is: 396 ÷ 66, 396 ÷ 99 and 396 ÷ 132 all come out whole. Any other common multiple of 66, 99 and 132 is a multiple of 396.

    See Also