how many packages of pencils and how many packages of erasers should Jason buy?

Question

pencils come in packages of 10. Erasers come in packages of 12. Jason wants to purchase the smallest number of pencils and erasers so that he will have exactly the same amount of pencils and erasers. 

Answer 1

Here are two ways to find the LCM (Least Common Multiple) of two numbers:

 

[1] list all of the multiples and choose the least common number

of 10:   10  20  30  40  50  60  70  80  90  100

of 12:   12  24  36  48  60  72  84  96

 

[2] find a number that shares all the prime factors of the two numbers

  (thus, is divisible by both of the numbers)

prime factors of 10:    2, 5

prime factors or 12:    2, 2, 3

LCM = 2*2*3*5 = 60

 

Jason should buy 6 packages of pencils (60) and 5 packages of erasers (60).