Math - LCM & GCF

Least Common Multiple (LCM)

Least common multiple (or LCM) is the process of finding the least common multiple of two or more numbers.

• LCM(5, 15) = 30

  Multiples of 5: $\{5,10,15,20,25,\textcolor{#7932ff}{30},35,40,45,50,55,60\}$
  Multiples of 15: $\{15,\textcolor{#7932ff}{30},45,60,75,90,105,120,135,150\}$

• LCM(8, 12, 9) = 72

  Multiples of 8: $\{8,16,24,32,40,48,56,64,\textcolor{#7932ff}{72},80\}$
  Multiples of 12: $\{12,24,36,48,60,\textcolor{#7932ff}{72},84,96,108,120\}$
  Multiples of 9: $\{9,18,27,36,45,54,63,\textcolor{#7932ff}{72},81,90\}$

Finding the LCM using the “Ladder” Method (youtube)

Greatest Common Factor (GCF)

Greatest common factor (or GCF) is the process of finding the greatest common factor of two or more numbers.

• GCF(140, 84) = 28

  Factors of 140 = $\{1,2,4,5,7,10,14,20,\textcolor{#7932ff}{28},35,70,140\}$
  Factors of 84 = $\{1,2,3,4,6,7,12,14,21,\textcolor{#7932ff}{28},42,84\}$

• GCF(9, 57, 78) = 3

  Factors of 9 = $\{1,\textcolor{#7932ff}{3},9\}$
  Factors of 57 = $\{1,\textcolor{#7932ff}{3},19,57\}$
  Factors of 78 = $\{1,2,\textcolor{#7932ff}{3},6,13,26,39,78\}$

Finding the GCF using the “Ladder” Method (youtube)