Question

Rachel planted periwinkles, lilies, tulips and primroses in $4$ different pots. The periwinkles bloom every 2 days, the lilies every $4$ days, the tulips every $6$ days and the primroses every $8$ days. If they bloomed together on the $1^{st}$ day of the month, then they will bloom together again on

• A. ${24}^{th}$ day of that month
• B. ${12}^{th}$ day of that month
• C. ${28}^{th}$ day of that month
• D. ${20}^{th}$ day of that month

Answer 1

The correct option is A ${24}^{th}$ day of that month

The four flowers bloom at an interval of $2,4,6$ and $8$ days, or at every multiple of $2,4,6$ and $8$ days. The number of days after which they bloom together is equal to the common multiples of $2,4,6$ and $8.$ The number of days after which they bloom together for the first time = LCM $(2,4,6$ and $8)$


Prime factorization of $2,4,6$ and $8:$
2 = 2
4 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2
$\therefore$ LCM = 24 = 2 × 2 × 2 × 3
Hence, they will bloom together again on the ${24}^{th}$ day of that month.