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    LCM for 9, 75 and 105

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

    What's the Least Common Multiple (LCM) of 9, 75 and 105?

    Answer

    LCM of 9, 75 and 105 is
    1,575

    (One thousand five hundred seventy-five)

    1,575 is the smallest positive integer that 9, 75 and 105 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 9, 75 and 105 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 75: 3 × 5 × 5 (exponent form: 3 × 52)

    All Prime Factors of 105: 3 × 5 × 7 (exponent form: 3 × 5 × 7)

    Prime factor975105Highest power
    3323332
    5—52552
    7——77

    LCM = 32 × 52 × 7 = 1,575

    Checking the LCM of 9, 75 and 105 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, 75) = (9 × 75) ÷ 3 = 675 ÷ 3 = 225

    LCM(225, 105) = (225 × 105) ÷ 15 = 23,625 ÷ 15 = 1,575

    LCM(9, 75, 105) = 1,575

    The pairs may be taken in any order — 75 and 105 first, then 9 — and the answer is the same 1,575. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 9, 75 and 105?. The LCM of 9, 75 and 105 is 1,575 — 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
    97590450
    9759120,475
    9759220,700
    975936,975
    9759421,150
    975954,275
    975967,200
    9759721,825
    9759822,050
    975992,475
    975100900
    97510122,725
    9751027,650
    97510323,175
    97510423,400
    9751051,575
    97510623,850
    97510724,075
    9751082,700
    97510924,525
    9751104,950
    9751118,325
    97511225,200
    97511325,425
    9751148,550
    9751155,175
    97511626,100
    9751172,925
    97511826,550
    97511926,775

    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, 75 and 105? (The answer is: 1,575). Enter the first number (e.g. '9'), the second (e.g. '75') and the third (e.g. '105'), 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, 75 and 105?

    LCM of 9, 75 and 105 is 1,575

    How to find the LCM of 9, 75 and 105 by prime factorization?

    Take every prime that appears in 9, 75 and 105 to the highest power it reaches in any one of them and multiply: 3² × 5² × 7 = 1,575.

    Can you get the LCM of 9, 75 and 105 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 9 and 75 is 225, and the LCM of 225 and 105 is 1,575 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,575 divisible by 9, 75 and 105?

    Yes, and by definition it is the smallest positive integer that is: 1,575 ÷ 9, 1,575 ÷ 75 and 1,575 ÷ 105 all come out whole. Any other common multiple of 9, 75 and 105 is a multiple of 1,575.

    See Also