Question

Rachel opens a biscuit factory. The biscuits of three varieties, A, B, and C, are manufactured.
Each packet has 12, 15, and 21 biscuits, respectively.

For quality check, she has to send packets of each variety such that the number of biscuits are equal.

Find the minimum number of biscuits of each variety sent for quality check.

• A. 420
• B. 210
• C. 840
• D. 180

Answer 1

The correct option is A 420

Number of biscuits of variety A in a packet = 12
Number of biscuits of variety B in a packet = 15
Number of biscuits of variety C in a packet = 21

To find the minimum number of biscuits Rachel sent, we will have to find the LCM of 12, 15, and 21.

$\text{Factors of 12}=2\times 2\times 3$
$\text{Factors of 15}=3\times 5$
$\text{Factors of 21}=3\times 7$
LCM of 12, 15, and 21
$=2\times 2\times 3\times 5\times 7$
$=420$

So, Rachel will place 420 biscuits of each variety.