LCM & HCF

LCM & HCF

1. the lowest common multiple is the smallest number that will divide by all the numbers in question

   • to find the LCM, list all the prime factors of a number, and then list all the prime factors that appear in both of the numbers, and multiply them all together to find the LCM
     • EXAMPLE:
       • find the LCM of 18 and 30
         • prime factors of 18 = 2 x 3 x 3
           • prime factors of 30 = 2 x 3 x 5
             • all the numbers that appear are 2, 3, 3, and 5
               • 2 x 3 x 3 x 5 is 90, so that is the LCM

2. the highest common factor is the biggest number that will divide into all the numbers in question

   • list all the prime factors that appear in each number, and find the common numbers and multiply them together to find the HCF
     • EXAMPLE:
       • find the HCF of 180 and 84
         • prime factors of 180 are 2, 2, 3, 3, and 5
           • prime factors of 84 are 2, 2, 3 and 7
           • common numbers are 2, 2, and 3
             • 2 x 2 x 3 is 12, this is your HCF