Topic outline

  • Playing With Numbers (Least Common Multiple (LCM)/ Lowest Common Multiple)

    • Lowest Common Multiple - Key Points Page

      Lowest Common Multiple (LCM)

      Lowest Common Multiple

      The Lowest Common Multiple (LCM) of two or more given number is the lowest (or smallest or least) of their common multiples.

      Example: LCM of 12 and 15.

      Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252…

      Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240…

      Common Multiples of 12 and 15 are 60, 120, 180, 240…

      Lowest Common Multiples of 12 and 15 is 60. (60 is the smallest number that both the numbers are factors of this number.)

       

      LCM by Prime Factorization Method

      Example: Find LCM of 16, 24 and 56

      Step1: Find out the prime factors of the given numbers.


      Prime factor of 24 = 2 x 2 x 2 x 3 = 23 x 3

      Prime factor of 56 = 2 x 2 x 2 x 7 = 23 x 7 

      Step2: Identify the maximum number of occurrence of each prime number. Here, 24 (2 has occurred 4 times), 31 (3 has occurred 1 time) and 71 (7 has occurred 1 time)

      Step3: Now multiply the outcomes.

      2 x 2 x 2 x 2 x 3 x 7 = 336

       

      LCM by Division Method

      Step 1: Find the prime factors of the two or more numbers by dividing the numbers by least prime number till we get 1. (Choose the least prime that at least divide one of the given numbers)

      Step 2: Then multiply all the prime factors to get the LCM.

      Example: Find LCM of 20, 25 and 30


      LCM of 20, 25 and 30 = 2 x 2 x 3 x 5 x 5 = 300

       

    • Lowest Common Multiple Worksheet 1 File

      Download to practice offline.


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