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    LCM for 15, 25 and 45

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

    What's the Least Common Multiple (LCM) of 15, 25 and 45?

    Answer

    LCM of 15, 25 and 45 is
    225

    (Two hundred twenty-five)

    225 is the smallest positive integer that 15, 25 and 45 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 25 and 45 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 15: 3 × 5 (exponent form: 3 × 5)

    All Prime Factors of 25: 5 × 5 (exponent form: 52)

    All Prime Factors of 45: 3 × 3 × 5 (exponent form: 32 × 5)

    Prime factor152545Highest power
    33—3232
    5552552

    LCM = 32 × 52 = 225

    Checking the LCM of 15, 25 and 45 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(15, 25) = (15 × 25) ÷ 5 = 375 ÷ 5 = 75

    LCM(75, 45) = (75 × 45) ÷ 15 = 3,375 ÷ 15 = 225

    LCM(15, 25, 45) = 225

    The pairs may be taken in any order — 25 and 45 first, then 15 — and the answer is the same 225. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 15, 25 and 45?. The LCM of 15, 25 and 45 is 225 — 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
    152530150
    1525312,325
    1525322,400
    152533825
    1525342,550
    152535525
    152536900
    1525372,775
    1525382,850
    152539975
    152540600
    1525413,075
    1525421,050
    1525433,225
    1525443,300
    152545225
    1525463,450
    1525473,525
    1525481,200
    1525493,675
    152550150
    1525511,275
    1525523,900
    1525533,975
    1525541,350
    152555825
    1525564,200
    1525571,425
    1525584,350
    1525594,425

    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 15, 25 and 45? (The answer is: 225). Enter the first number (e.g. '15'), the second (e.g. '25') and the third (e.g. '45'), 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 15, 25 and 45?

    LCM of 15, 25 and 45 is 225

    How to find the LCM of 15, 25 and 45 by prime factorization?

    Take every prime that appears in 15, 25 and 45 to the highest power it reaches in any one of them and multiply: 3² × 5² = 225.

    Can you get the LCM of 15, 25 and 45 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 25 is 75, and the LCM of 75 and 45 is 225 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 225 divisible by 15, 25 and 45?

    Yes, and by definition it is the smallest positive integer that is: 225 ÷ 15, 225 ÷ 25 and 225 ÷ 45 all come out whole. Any other common multiple of 15, 25 and 45 is a multiple of 225.

    See Also