Question

Rachel planted periwinkle, lilies, tulips and primroses in four different pots. The periwinkle bloom every 2 days, the lilies every 4 days, the tulips every 6 days, and the primroses every 8 days. If all the flowers bloomed together on the first day of the month, will they bloom together again before the end of the month?

• A. yes
• B. no

Answer 1

The correct option is A yes

The LCM of 2, 4, 6, and 8 gives the date on which those four flowers will bloom.

Let's find the LCM using prime factorizations of 2, 4, 6 and 8 are:
2 = 2
4 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2

LCM is the product of maximum occurrences of each prime factor in the given numbers.

So LCM(2, 4, 6, 8) = 2 × 2 × 2 × 3 = 24 days

All the flowers will bloom again 24 days later. Hence, they will all bloom together before the end of the month.