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    LCM for 9, 10 and 28

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

    What's the Least Common Multiple (LCM) of 9, 10 and 28?

    Answer

    LCM of 9, 10 and 28 is
    1,260

    (One thousand two hundred sixty)

    1,260 is the smallest positive integer that 9, 10 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 9, 10 and 28 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 9: 3 × 3 (exponent form: 32)

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

    Prime factor91028Highest power
    2—22222
    332——32
    5—5—5
    7——77

    LCM = 22 × 32 × 5 × 7 = 1,260

    Checking the LCM of 9, 10 and 28 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(9, 10) = (9 × 10) ÷ 1 = 90 ÷ 1 = 90

    LCM(90, 28) = (90 × 28) ÷ 2 = 2,520 ÷ 2 = 1,260

    LCM(9, 10, 28) = 1,260

    The pairs may be taken in any order — 10 and 28 first, then 9 — and the answer is the same 1,260. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 9, 10 and 28?. The LCM of 9, 10 and 28 is 1,260 — 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
    910131,170
    91014630
    9101590
    91016720
    910171,530
    9101890
    910191,710
    91020180
    91021630
    91022990
    910232,070
    91024360
    91025450
    910261,170
    91027270
    910281,260
    910292,610
    9103090
    910312,790
    910321,440
    91033990
    910341,530
    91035630
    91036180
    910373,330
    910381,710
    910391,170
    91040360
    910413,690
    91042630

    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 9, 10 and 28? (The answer is: 1,260). Enter the first number (e.g. '9'), the second (e.g. '10') and the third (e.g. '28'), 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 9, 10 and 28?

    LCM of 9, 10 and 28 is 1,260

    How to find the LCM of 9, 10 and 28 by prime factorization?

    Take every prime that appears in 9, 10 and 28 to the highest power it reaches in any one of them and multiply: 2² × 3² × 5 × 7 = 1,260.

    Can you get the LCM of 9, 10 and 28 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 9 and 10 is 90, and the LCM of 90 and 28 is 1,260 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,260 divisible by 9, 10 and 28?

    Yes, and by definition it is the smallest positive integer that is: 1,260 ÷ 9, 1,260 ÷ 10 and 1,260 ÷ 28 all come out whole. Any other common multiple of 9, 10 and 28 is a multiple of 1,260.

    See Also