Question

At a local bank, certificates of deposit mature every 9 months. At another bank, CDs mature every 12 months. If CDs are purchased at each bank and are renewed when they mature, what is the least number of months that will pass before the two CDs mature at the same time?

a. 27 months
b. 36 months
c. 45 months
d. 54 months

Answer 1

The least common multiple of 9 and 12 is 36 months.

Step-by-step explanation:

To find the least number of months that will pass before the two CDs mature at the same time, we need to find the least common multiple (LCM) of 9 and 12.

1. Find the prime factors of both numbers. For 9: 3 x 3. For 12: 2 x 2 x 3.
2. Take the highest power of each prime factor: 3^2 x 2^2 = 36.

Therefore, the least number of months that will pass before the two CDs mature at the same time is 36 months.