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    LCM for 15, 40 and 60

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

    What's the Least Common Multiple (LCM) of 15, 40 and 60?

    Answer

    LCM of 15, 40 and 60 is
    120

    (One hundred twenty)

    120 is the smallest positive integer that 15, 40 and 60 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 15, 40 and 60 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 40: 2 × 2 × 2 × 5 (exponent form: 23 × 5)

    All Prime Factors of 60: 2 × 2 × 3 × 5 (exponent form: 22 × 3 × 5)

    Prime factor154060Highest power
    2—232223
    33—33
    55555

    LCM = 23 × 3 × 5 = 120

    Checking the LCM of 15, 40 and 60 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, 40) = (15 × 40) ÷ 5 = 600 ÷ 5 = 120

    LCM(120, 60) = (120 × 60) ÷ 60 = 7,200 ÷ 60 = 120

    LCM(15, 40, 60) = 120

    The pairs may be taken in any order — 40 and 60 first, then 15 — and the answer is the same 120. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 15, 40 and 60?. The LCM of 15, 40 and 60 is 120 — 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
    154045360
    1540462,760
    1540475,640
    154048240
    1540495,880
    154050600
    1540512,040
    1540521,560
    1540536,360
    1540541,080
    1540551,320
    154056840
    1540572,280
    1540583,480
    1540597,080
    154060120
    1540617,320
    1540623,720
    1540632,520
    154064960
    1540651,560
    1540661,320
    1540678,040
    1540682,040
    1540692,760
    154070840
    1540718,520
    154072360
    1540738,760
    1540744,440

    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, 40 and 60? (The answer is: 120). Enter the first number (e.g. '15'), the second (e.g. '40') and the third (e.g. '60'), 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, 40 and 60?

    LCM of 15, 40 and 60 is 120

    How to find the LCM of 15, 40 and 60 by prime factorization?

    Take every prime that appears in 15, 40 and 60 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 = 120.

    Can you get the LCM of 15, 40 and 60 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 15 and 40 is 120, and the LCM of 120 and 60 is 120 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 120 divisible by 15, 40 and 60?

    Yes, and by definition it is the smallest positive integer that is: 120 ÷ 15, 120 ÷ 40 and 120 ÷ 60 all come out whole. Any other common multiple of 15, 40 and 60 is a multiple of 120.

    See Also