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    LCM for 3, 5 and 20

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

    What's the Least Common Multiple (LCM) of 3, 5 and 20?

    Answer

    LCM of 3, 5 and 20 is
    60

    (Sixty)

    60 is the smallest positive integer that 3, 5 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 3, 5 and 20 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 3: 3 (exponent form: 3)

    All Prime Factors of 5: 5 (exponent form: 5)

    All Prime Factors of 20: 2 × 2 × 5 (exponent form: 22 × 5)

    Prime factor3520Highest power
    2——2222
    33——3
    5—555

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 3, 5 and 20 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(3, 5) = (3 × 5) ÷ 1 = 15 ÷ 1 = 15

    LCM(15, 20) = (15 × 20) ÷ 5 = 300 ÷ 5 = 60

    LCM(3, 5, 20) = 60

    The pairs may be taken in any order — 5 and 20 first, then 3 — and the answer is the same 60. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 3, 5 and 20?. The LCM of 3, 5 and 20 is 60 — 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
    35515
    35630
    357105
    358120
    35945
    351030
    3511165
    351260
    3513195
    3514210
    351515
    3516240
    3517255
    351890
    3519285
    352060
    3521105
    3522330
    3523345
    3524120
    352575
    3526390
    3527135
    3528420
    3529435
    353030
    3531465
    3532480
    3533165
    3534510

    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 3, 5 and 20? (The answer is: 60). Enter the first number (e.g. '3'), the second (e.g. '5') and the third (e.g. '20'), 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 3, 5 and 20?

    LCM of 3, 5 and 20 is 60

    How to find the LCM of 3, 5 and 20 by prime factorization?

    Take every prime that appears in 3, 5 and 20 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

    Can you get the LCM of 3, 5 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 3 and 5 is 15, and the LCM of 15 and 20 is 60 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 60 divisible by 3, 5 and 20?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 3, 60 ÷ 5 and 60 ÷ 20 all come out whole. Any other common multiple of 3, 5 and 20 is a multiple of 60.

    See Also