word problem algebra

Question

Two cousins visited Jane today. One cousin visits every 42 days. The other
visits every 429 days. They will next visit on the same day in __?__ days.

Answer 1

To solve this problem, you need to find the least common multiple of 42 and 429; in other words, what is the smallest number that can be divided by both numbers evenly.  To do this, find the prime factors of each number and multiply them together, but don't duplicate any that are found in both.

 

42:  2, 3, 7

429:  3, 11, 13

 

2x3x7x11x13 = 6006

 

The answer is 6006 days.  Notice that 3 was a common factor of both numbers, so it was used only once.