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 8, 10 and 20

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

    What's the Least Common Multiple (LCM) of 8, 10 and 20?

    Answer

    LCM of 8, 10 and 20 is
    40

    (Forty)

    40 is the smallest positive integer that 8, 10 and 20 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 8, 10 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 8: 2 × 2 × 2 (exponent form: 23)

    All Prime Factors of 10: 2 × 5 (exponent form: 2 × 5)

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

    Prime factor81020Highest power
    22322223
    5—555

    LCM = 23 × 5 = 40

    Checking the LCM of 8, 10 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(8, 10) = (8 × 10) ÷ 2 = 80 ÷ 2 = 40

    LCM(40, 20) = (40 × 20) ÷ 20 = 800 ÷ 20 = 40

    LCM(8, 10, 20) = 40

    The pairs may be taken in any order — 10 and 20 first, then 8 — and the answer is the same 40. 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/8--10--20Copy
    <a href="https://calculat.io/en/number/least-common-multiple-lcm-of-3-numbers/8--10--20">What is the LCM of 8, 10 and 20? - Calculatio</a>Copy
    Facebook
    Twitter
    Telegram
    WhatsApp
    Viber
    Email
    What is the LCM of 8, 10 and 20?. The LCM of 8, 10 and 20 is 40 — 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/8--10--20/generated.jpgCopy

    LCM Table

    Number 1Number 2Number 3LCM
    581040
    6810120
    7810280
    881040
    8910360
    8101040
    81011440
    81012120
    81013520
    81014280
    81015120
    8101680
    81017680
    81018360
    81019760
    8102040
    81021840
    81022440
    81023920
    81024120
    81025200
    81026520
    810271,080
    81028280
    810291,160
    81030120
    810311,240
    81032160
    810331,320
    81034680

    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 8, 10 and 20? (The answer is: 40). Enter the first number (e.g. '8'), the second (e.g. '10') 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 8, 10 and 20?

    LCM of 8, 10 and 20 is 40

    How to find the LCM of 8, 10 and 20 by prime factorization?

    Take every prime that appears in 8, 10 and 20 to the highest power it reaches in any one of them and multiply: 2³ × 5 = 40.

    Can you get the LCM of 8, 10 and 20 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 8 and 10 is 40, and the LCM of 40 and 20 is 40 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 40 divisible by 8, 10 and 20?

    Yes, and by definition it is the smallest positive integer that is: 40 ÷ 8, 40 ÷ 10 and 40 ÷ 20 all come out whole. Any other common multiple of 8, 10 and 20 is a multiple of 40.

    See Also