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    LCM for 10, 100 and 1,000

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

    What's the Least Common Multiple (LCM) of 10, 100 and 1,000?

    Answer

    LCM of 10, 100 and 1,000 is
    1,000

    (One thousand)

    1,000 is the smallest positive integer that 10, 100 and 1,000 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 10, 100 and 1,000 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 10: 2 × 5 (exponent form: 2 × 5)

    All Prime Factors of 100: 2 × 2 × 5 × 5 (exponent form: 22 × 52)

    All Prime Factors of 1,000: 2 × 2 × 2 × 5 × 5 × 5 (exponent form: 23 × 53)

    Prime factor101001,000Highest power
    22222323
    55525353

    LCM = 23 × 53 = 1,000

    Checking the LCM of 10, 100 and 1,000 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(10, 100) = (10 × 100) ÷ 10 = 1,000 ÷ 10 = 100

    LCM(100, 1,000) = (100 × 1,000) ÷ 100 = 100,000 ÷ 100 = 1,000

    LCM(10, 100, 1,000) = 1,000

    The pairs may be taken in any order — 100 and 1,000 first, then 10 — and the answer is the same 1,000. That is exactly why the two routes on this page agree.

    Related Calculations

    See Also

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    What is the LCM of 10, 100 and 1,000?. The LCM of 10, 100 and 1,000 is 1,000 — 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
    1010098519,700
    1010098649,300
    1010098798,700
    1010098824,700
    1010098998,900
    101009909,900
    1010099199,100
    1010099224,800
    1010099399,300
    1010099449,700
    1010099519,900
    1010099624,900
    1010099799,700
    1010099849,900
    1010099999,900
    101001,0001,000
    101001,001100,100
    101001,00250,100
    101001,003100,300
    101001,00425,100
    101001,00520,100
    101001,00650,300
    101001,007100,700
    101001,00825,200
    101001,009100,900
    101001,01010,100
    101001,011101,100
    101001,01225,300
    101001,013101,300
    101001,01450,700

    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 10, 100 and 1,000? (The answer is: 1,000). Enter the first number (e.g. '10'), the second (e.g. '100') and the third (e.g. '1,000'), 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 10, 100 and 1,000?

    LCM of 10, 100 and 1,000 is 1,000

    How to find the LCM of 10, 100 and 1,000 by prime factorization?

    Take every prime that appears in 10, 100 and 1,000 to the highest power it reaches in any one of them and multiply: 2³ × 5³ = 1,000.

    Can you get the LCM of 10, 100 and 1,000 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 10 and 100 is 100, and the LCM of 100 and 1,000 is 1,000 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 1,000 divisible by 10, 100 and 1,000?

    Yes, and by definition it is the smallest positive integer that is: 1,000 ÷ 10, 1,000 ÷ 100 and 1,000 ÷ 1,000 all come out whole. Any other common multiple of 10, 100 and 1,000 is a multiple of 1,000.

    See Also