Basic(Elementary) Mathematics

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Greatest Common Factor and Least Common Multiple

Greatest Common Factor(GCF) is the largest number that can divide set or pair of numbers with out a remainder. Example: The GCF of 4 and 10 is 2, because 2 can both divide 4 and 10 with out a remainder.
Least Common Multiple(LCM) is the smallest number divisible by a set or pair of numbers. Example: The LCM of 4 and 10 is 40, because 40 is divisible by both 10 and 4.

Sample Calculations:

  1. Find the GCF and LCM of 80, 120, 160
    2. Number Prime Factors
    80 2 x 2 x 2 x 2 x 5
    120 2 x 2 x 2 x 3 x 5
    160 2 x 2 x 2 x 2 x 2 x 5
    Similar factors: 5 x 2 x 2 x 2 = 40. Thus the GCF is 40
    Factors: 5 x 2 x 2 x 2 x 2 x 2 x 3= 480. Thus the LCM is 480
    lcm and gcf
  2. Find the GCF of 45 and 60
    3. Number Prime Factors
    45 5 x 3 x 3
    60 5 x 3 x 2 x 2
    Similar factors: 5 x 3 = 15. Thus the GCF is 15
    Factors: 5 x 3 x 3 x 2 x 2 = 180. Thus the LCM is 180