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 4, 5 and 6

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

    What's the Least Common Multiple (LCM) of 4, 5 and 6?

    Answer

    LCM of 4, 5 and 6 is
    60

    (Sixty)

    60 is the smallest positive integer that 4, 5 and 6 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 5 and 6 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 4: 2 × 2 (exponent form: 22)

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

    All Prime Factors of 6: 2 × 3 (exponent form: 2 × 3)

    Prime factor456Highest power
    222—222
    3——33
    5—5—5

    LCM = 22 × 3 × 5 = 60

    Checking the LCM of 4, 5 and 6 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(4, 5) = (4 × 5) ÷ 1 = 20 ÷ 1 = 20

    LCM(20, 6) = (20 × 6) ÷ 2 = 120 ÷ 2 = 60

    LCM(4, 5, 6) = 60

    The pairs may be taken in any order — 5 and 6 first, then 4 — and the answer is the same 60. 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/4--5--6Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/4--5--6">What is the LCM of 4, 5 and 6? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 4, 5 and 6?. The LCM of 4, 5 and 6 is 60 — 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/4--5--6/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    14520
    24520
    34560
    44520
    45520
    45660
    457140
    45840
    459180
    451020
    4511220
    451260
    4513260
    4514140
    451560
    451680
    4517340
    4518180
    4519380
    452020
    4521420
    4522220
    4523460
    4524120
    4525100
    4526260
    4527540
    4528140
    4529580
    453060

    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 4, 5 and 6? (The answer is: 60). Enter the first number (e.g. '4'), the second (e.g. '5') and the third (e.g. '6'), 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 4, 5 and 6?

    LCM of 4, 5 and 6 is 60

    How to find the LCM of 4, 5 and 6 by prime factorization?

    Take every prime that appears in 4, 5 and 6 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 = 60.

    Can you get the LCM of 4, 5 and 6 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 5 is 20, and the LCM of 20 and 6 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 4, 5 and 6?

    Yes, and by definition it is the smallest positive integer that is: 60 ÷ 4, 60 ÷ 5 and 60 ÷ 6 all come out whole. Any other common multiple of 4, 5 and 6 is a multiple of 60.

    See Also