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    LCM for 4, 10 and 50

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

    What's the Least Common Multiple (LCM) of 4, 10 and 50?

    Answer

    LCM of 4, 10 and 50 is
    100

    (One hundred)

    100 is the smallest positive integer that 4, 10 and 50 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 4, 10 and 50 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 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

    Prime factor41050Highest power
    2222222
    5—55252

    LCM = 22 × 52 = 100

    Checking the LCM of 4, 10 and 50 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, 10) = (4 × 10) ÷ 2 = 40 ÷ 2 = 20

    LCM(20, 50) = (20 × 50) ÷ 10 = 1,000 ÷ 10 = 100

    LCM(4, 10, 50) = 100

    The pairs may be taken in any order — 10 and 50 first, then 4 — and the answer is the same 100. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 4, 10 and 50?. The LCM of 4, 10 and 50 is 100 — 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
    41035140
    41036180
    41037740
    41038380
    41039780
    4104040
    41041820
    41042420
    41043860
    41044220
    41045180
    41046460
    41047940
    41048240
    41049980
    41050100
    410511,020
    41052260
    410531,060
    41054540
    41055220
    41056280
    410571,140
    41058580
    410591,180
    4106060
    410611,220
    41062620
    410631,260
    41064320

    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, 10 and 50? (The answer is: 100). Enter the first number (e.g. '4'), the second (e.g. '10') and the third (e.g. '50'), 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, 10 and 50?

    LCM of 4, 10 and 50 is 100

    How to find the LCM of 4, 10 and 50 by prime factorization?

    Take every prime that appears in 4, 10 and 50 to the highest power it reaches in any one of them and multiply: 2² × 5² = 100.

    Can you get the LCM of 4, 10 and 50 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 4 and 10 is 20, and the LCM of 20 and 50 is 100 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 100 divisible by 4, 10 and 50?

    Yes, and by definition it is the smallest positive integer that is: 100 ÷ 4, 100 ÷ 10 and 100 ÷ 50 all come out whole. Any other common multiple of 4, 10 and 50 is a multiple of 100.

    See Also