Question

Jim changes his password every 90 days and cleans out his files every 50 days. If he just did both on the same day, how many days until he does both again on the same day?

Answer 1

450

Explanation:

this question requires us to find the least common multiple of 90 and 50

let's take the first 5 multiples of each and see if we find one in common:

90, 180, 270, 360, 450, 540

50, 100, 150, 200, 250, 300

we can use another method by breaking down each number into a product of its prime numbers:

90 = 5 x 18 = 5 x 2 x 9 = 5 x 2 x 3²

50 = 5 x 10 = 5² x 2

take out any numbers they have in common, which are:

one 2 and one 5

take out any numbers they do not have in common, which are:

2 and 5 and 3²

multiply the ones in common ⇒ 2 x 5 = 10

multiply the ones not common ⇒ 2 x 5 x 3² = 45

multiply 10 and 45 to get the least common multiple of 450