Interesting Facts about LCM

Last Updated : 23 Jul, 2025

LCM (Least Common Multiple) of two or more numbers is the smallest number that is divisible by each of the given numbers (resulting in a remainder of 0 when we divide the LCM by the given numbers).

To find the LCM of 3 and 5, we list the multiples of both numbers:

  • Multiples of 3: 3, 6, 9, 12, 15, 18, . . .
  • Multiples of 5: 5, 10, 15, 20, 25, . . .

By comparing the multiples of 3 and 5, we find that the lowest number that is a multiple of both 3 and 5 is 15. Thus, the LCM of 3 and 5 is 15.

Some of the important facts on to LCM ( Least Common Multiple) are:

  • The LCM of any number and 1 is always the number itself, as 1 is a factor of every integer.
  • When calculating the LCM of two prime numbers, the result is simply their product since prime numbers doesn't share any common factors other than 1.
  • LCM (Least Common Multiple) of a number and its multiple is multiple itself, as it is the smallest multiple that both the number and the multiple share.
  • If two numbers are coprime (having no common factors other than 1), their LCM is equal to their product.
  • The LCM of two consecutive integers is always their product, as consecutive integers share no common factors other than 1.
  • For more than two numbers, the LCM can be calculated sequentially, starting with the first two numbers and then incorporating the next number, using the formula:
    • LCM (a, b, c) = LCM (LCM (a, b), c).
  • LCM of the first 10 natural numbers is 2520.
  • LCM is always greater than or equal to the largest number in a problem.
  • The product of GCD and LCM of two natural numbers is always equal to the product of numbers i.e., LCM (a, b) × GCD (a, b) = a × b.
  • LCM is always divisible by GCD.
  • The LCM of an EVEN number and another EVEN will always be even.
  • The LCM of an ODD number and EVEN number will always be even.
  • If two numbers are factors and multiples of each other, the smaller number is the HCF (Highest Common Factor), and the larger number is the LCM (Least Common Multiple).
  • The HCF (Highest Common Factor) of two or more numbers is always a factor of their LCM (Least Common Multiple).
  • To find the LCM of fractions, you calculate the LCM of the numerators and divide it by the HCF of the denominators.
  • GCD and LCM distribute over each other.
    GCD(a, LCM(b, c)) = GCD(LCM(a, b), LCM(a, c)) and
    LCM(a, GCD(b, c)) = LCM(GCD(a, b), GCD(a, c))

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