Mike can buy red push pins in packages of 10 and yellow push pins in packages of 12. What is the least amount of packages of each color he must buy in order to have the same number of pins

6 packages of red push pins

5 packages of yellow push pins

Step-by-step explanation:

The goal is to list the multiples of 10 and 12 and find the least common multiple (LCM) to answer the question.

The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 ...

The multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 ...

The first multiple that 10 and 12 have in common is 60. Therefore, Mike must buy at least 6 packages of red push pins [60 : 10 = 6] and 5 packages of yellow push pins [60 : 12 = 5] to have the same number of pins of each color.