Feedback form
Hi! What do you think?

Drag it here or paste with Ctrl+V

    You can also email us on infocalculat.io

    LCM for 30, 36 and 48

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

    What's the Least Common Multiple (LCM) of 30, 36 and 48?

    Answer

    LCM of 30, 36 and 48 is
    720

    (Seven hundred twenty)

    720 is the smallest positive integer that 30, 36 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 30, 36 and 48 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 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

    All Prime Factors of 36: 2 × 2 × 3 × 3 (exponent form: 22 × 32)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    Prime factor303648Highest power
    22222424
    3332332
    55——5

    LCM = 24 × 32 × 5 = 720

    Checking the LCM of 30, 36 and 48 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(30, 36) = (30 × 36) ÷ 6 = 1,080 ÷ 6 = 180

    LCM(180, 48) = (180 × 48) ÷ 12 = 8,640 ÷ 12 = 720

    LCM(30, 36, 48) = 720

    The pairs may be taken in any order — 36 and 48 first, then 30 — and the answer is the same 720. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

    Share This Calculation
    Print
    https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/30--36--48Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/30--36--48">What is the LCM of 30, 36 and 48? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 30, 36 and 48?. The LCM of 30, 36 and 48 is 720 — 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/30--36--48/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    3033361,980
    3034363,060
    3035361,260
    303636180
    3036376,660
    3036383,420
    3036392,340
    303640360
    3036417,380
    3036421,260
    3036437,740
    3036441,980
    303645180
    3036464,140
    3036478,460
    303648720
    3036498,820
    303650900
    3036513,060
    3036522,340
    3036539,540
    303654540
    3036551,980
    3036562,520
    3036573,420
    3036585,220
    30365910,620
    303660180
    30366110,980
    3036625,580

    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 30, 36 and 48? (The answer is: 720). Enter the first number (e.g. '30'), the second (e.g. '36') and the third (e.g. '48'), 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 30, 36 and 48?

    LCM of 30, 36 and 48 is 720

    How to find the LCM of 30, 36 and 48 by prime factorization?

    Take every prime that appears in 30, 36 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3² × 5 = 720.

    Can you get the LCM of 30, 36 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 30 and 36 is 180, and the LCM of 180 and 48 is 720 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 720 divisible by 30, 36 and 48?

    Yes, and by definition it is the smallest positive integer that is: 720 ÷ 30, 720 ÷ 36 and 720 ÷ 48 all come out whole. Any other common multiple of 30, 36 and 48 is a multiple of 720.

    See Also