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    LCM for 10, 22 and 99

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

    What's the Least Common Multiple (LCM) of 10, 22 and 99?

    Answer

    LCM of 10, 22 and 99 is
    990

    (Nine hundred ninety)

    990 is the smallest positive integer that 10, 22 and 99 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 22 and 99 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 10: 2 × 5 (exponent form: 2 × 5)

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

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

    Prime factor102299Highest power
    222—2
    3——3232
    55——5
    11—111111

    LCM = 2 × 32 × 5 × 11 = 990

    Checking the LCM of 10, 22 and 99 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(10, 22) = (10 × 22) ÷ 2 = 220 ÷ 2 = 110

    LCM(110, 99) = (110 × 99) ÷ 11 = 10,890 ÷ 11 = 990

    LCM(10, 22, 99) = 990

    The pairs may be taken in any order — 22 and 99 first, then 10 — and the answer is the same 990. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 10, 22 and 99?. The LCM of 10, 22 and 99 is 990 — 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
    1022844,620
    1022851,870
    1022864,730
    1022879,570
    102288440
    1022899,790
    102290990
    10229110,010
    1022925,060
    10229310,230
    1022945,170
    1022952,090
    1022965,280
    10229710,670
    1022985,390
    102299990
    10221001,100
    102210111,110
    10221025,610
    102210311,330
    10221045,720
    10221052,310
    10221065,830
    102210711,770
    10221085,940
    102210911,990
    1022110110
    102211112,210
    10221126,160
    102211312,430

    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 10, 22 and 99? (The answer is: 990). Enter the first number (e.g. '10'), the second (e.g. '22') and the third (e.g. '99'), 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 10, 22 and 99?

    LCM of 10, 22 and 99 is 990

    How to find the LCM of 10, 22 and 99 by prime factorization?

    Take every prime that appears in 10, 22 and 99 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 11 = 990.

    Can you get the LCM of 10, 22 and 99 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 22 is 110, and the LCM of 110 and 99 is 990 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 990 divisible by 10, 22 and 99?

    Yes, and by definition it is the smallest positive integer that is: 990 ÷ 10, 990 ÷ 22 and 990 ÷ 99 all come out whole. Any other common multiple of 10, 22 and 99 is a multiple of 990.

    See Also