What is the gcf and LCM of 125 and 40?

Answer 1

Write 125 and 40 as their prime factorizations (in power notation):

125 = 53

40 = 23 x 5

Then for gcf, use the lowest power of each prime across the numbers (if a prime doesn't appear in a number, its power is 0 and p0 = 1):

gcf = 20 x 51

= 1 x 5

= 5

For lcm, use the highest power of each prime across the numbers:

lcm = 23 x 53

= 8 x 125

= 1000