LCM of 0 and 0, the Least (Lowest) Common Multiple Calculator

Calculator of the LCM of 0 and 0, the least (lowest) common multiple of the numbers

What is the least common multiple (LCM)?

  • The least common multiple (LCM) of two numbers is the smallest non zero natural number that is a multiple of both numbers.
  • For example, the LCM of 2 and 3 is 6.

  • Other multiples of two numbers

  • Once you have calculated the LCM of two numbers, you can find other multiples of these two numbers by multiplying LCM by any other natural number.
  • For example, the LCM of 2 and 3 = 6, then the following numbers are also multiples of the numbers 2 and 3: 6 × 0 = 0; 6 × 2 = 12; 6 × 3 = 18; ... and so on.
  • There are infinitely many multiples of any two numbers.

  • The common denominator of two fractions

  • Calculating the common denominator of two fractions is equivalent to calculating the lowest common multiple (LCM) of their denominators.
  • By example: in order to add two fractions, 1/2 and 1/3, we need them to have the same denominator, preferable as small as possible. Well, this common denominator is 6, the least common multiple of 2 and 3: 1/2 + 1/3 = (3 × 1) / 6 + (2 × 1) / 6 = 3/6 + 2/6 = 5/6
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lcm (0; 0) = ?

Special case: both numbers are zero.

The only multiple of 0 and 0 is 0. So if the LCM (0; 0) existed, it would be 0.

However, by definition, the least common multiple of two numbers is the smallest non-zero natural number that is a multiple of both.

If zero were considered valid, then it would be the least common multiple of all numbers.


The answer
lcm (0; 0) = undefined


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The least common multiple (lcm). What it is and how to calculate it.

  • The number 60 is a common multiple of the numbers 6 and 15 because 60 is a multiple of 6 (60 = 6 × 10) and also a multiple of 15 (60 = 15 × 4).
  • There are infinitely many common multiples of 6 and 15.
  • If the number "v" is a multiple of the numbers "a" and "b", then all the multiples of "v" are also multiples of "a" and "b".
  • The common multiples of 6 and 15 are the numbers 30, 60, 90, 120, and so on.
  • Out of these, 30 is the smallest, 30 is the least common multiple (lcm) of 6 and 15.
  • Note: The prime factorization of a number: finding the prime numbers that multiply together to give that number.
  • If e = lcm (a, b), then the prime factorization of "e" must contain all the prime factors involved in the prime factorization of "a" and "b" taken by the highest power.
  • Example:
  • 40 = 23 × 5
  • 36 = 22 × 32
  • 126 = 2 × 32 × 7
  • lcm (40, 36, 126) = 23 × 32 × 5 × 7 = 2,520
  • Note: 23 = 2 × 2 × 2 = 8. We are saying that 2 was raised to the power of 3. Or, shorter, 2 to the power of 3. In this example 3 is the exponent and 2 is the base. The exponent indicates how many times the base is multiplied by itself. 23 is the power and 8 is the value of the power:
  • Another example of calculating the least common multiple, lcm:
  • 938 = 2 × 7 × 67
  • 982 = 2 × 491
  • 743 = is a prime number and cannot be broken down into other prime factors
  • lcm (938, 982, 743) = 2 × 7 × 67 × 491 × 743 = 342,194,594
  • If two or more numbers have no common factors (they are coprime), then their least common multiple is calculated by simply multiplying the numbers.
  • Example:
  • 6 = 2 × 3
  • 35 = 5 × 7
  • lcm (6, 35) = 2 × 3 × 5 × 7 = 6 × 35 = 210