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    LCM for 45, 135 and 225

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

    What's the Least Common Multiple (LCM) of 45, 135 and 225?

    Answer

    LCM of 45, 135 and 225 is
    675

    (Six hundred seventy-five)

    675 is the smallest positive integer that 45, 135 and 225 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 45, 135 and 225 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 45: 3 × 3 × 5 (exponent form: 32 × 5)

    All Prime Factors of 135: 3 × 3 × 3 × 5 (exponent form: 33 × 5)

    All Prime Factors of 225: 3 × 3 × 5 × 5 (exponent form: 32 × 52)

    Prime factor45135225Highest power
    332333233
    5555252

    LCM = 33 × 52 = 675

    Checking the LCM of 45, 135 and 225 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(45, 135) = (45 × 135) ÷ 45 = 6,075 ÷ 45 = 135

    LCM(135, 225) = (135 × 225) ÷ 45 = 30,375 ÷ 45 = 675

    LCM(45, 135, 225) = 675

    The pairs may be taken in any order — 135 and 225 first, then 45 — and the answer is the same 675. That is exactly why the two routes on this page agree.

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    What is the LCM of 45, 135 and 225?. The LCM of 45, 135 and 225 is 675 — 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
    451352101,890
    4513521128,485
    4513521228,620
    451352139,585
    4513521428,890
    451352155,805
    451352161,080
    4513521729,295
    4513521829,430
    451352199,855
    451352205,940
    4513522129,835
    451352229,990
    4513522330,105
    4513522430,240
    45135225675
    4513522630,510
    4513522730,645
    4513522810,260
    4513522930,915
    451352306,210
    4513523110,395
    4513523231,320
    4513523331,455
    451352343,510
    451352356,345
    4513523631,860
    4513523710,665
    4513523832,130
    4513523932,265

    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 45, 135 and 225? (The answer is: 675). Enter the first number (e.g. '45'), the second (e.g. '135') and the third (e.g. '225'), 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 45, 135 and 225?

    LCM of 45, 135 and 225 is 675

    How to find the LCM of 45, 135 and 225 by prime factorization?

    Take every prime that appears in 45, 135 and 225 to the highest power it reaches in any one of them and multiply: 3³ × 5² = 675.

    Can you get the LCM of 45, 135 and 225 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 45 and 135 is 135, and the LCM of 135 and 225 is 675 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 675 divisible by 45, 135 and 225?

    Yes, and by definition it is the smallest positive integer that is: 675 ÷ 45, 675 ÷ 135 and 675 ÷ 225 all come out whole. Any other common multiple of 45, 135 and 225 is a multiple of 675.

    See Also