Formulas for LCM Questions

Formulas for Lowest Common Multiple (LCM)

LCM stands for Least Common Multiple or Lowest Common Multiple. The Lowest Common Multiple is the smallest positive integer that is evenly divisible by both two or more integers. The page consists Definition, Method to calculate LCM and Formulas for LCM .

LCM Formula

Definition & Formula

  • LCM: Least Common Multiple is a number which is multiple of two or more than two numbers.

  • LCM of fractions = \frac{L.C.M of numerators}{ H.C.F of denominators}

  • The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into.

Methods to calculate LCM

  • Prime factorization
    • We multiply the prime factors with the highest powers to get the LCM.
    • For example: Find the LCM of 12 and 30
    • Prime factorization of 12 = 2 * 2 * 3 = 22 * 31 * 50
    • Prime factorization of 30 = 2 * 3 * 5 = 21 * 31 * 51
    • Highest exponent value we take 22 * 31 * 51 = 60
    • Therefore, LCM (12, 30) = 60
  • Line division

    • The LCM (12, 30) = 22 × 31 × 51 = 60

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