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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

    First common multiples: 1,575; 3,150; 4,725; …

    1,575 is divisible by all three: 1,575 ÷ 9 = 175; 1,575 ÷ 75 = 21; 1,575 ÷ 105 = 15 — and 175, 21 and 15 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/9 by 175 and of y/75 by 21 and of z/105 by 15.

    9 = 32

    75 = 3 × 52

    105 = 3 × 5 × 7

    Prime975105Highest power
    3323332
    5—52552
    7——77

    — = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

    LCM = 32 × 52 × 7 = 1,575

    More with these numbers

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    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--75--105Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--75--105">What is the LCM of 9, 75 and 105? - Calculatio</a>Copy
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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.
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/9--75--105/generated.jpgCopy

    LCM Table

    1st2nd3rdLCM
    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

    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. 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