Question

Question 194

Three brands A, B and C of biscuits are available in packets of 12,15, and 21 biscuits, respectively. If a shopkeeper wants to buy an equal number of biscuits of each brand, what is the minimum number of packets of each brand, he should buy?

Answer 1

Here, the minimum number of packets of each brand that the shopkeeper should buy is equal to the LCM of 12, 15 and 21.

So, LCM of 12,15 and 21 by division method,
$\begin{array}{cc}2& 12,15,21\\ 2& 6,15,21\\ 3& 3,15,21\\ 5& 1,5,7\\ 7& 1,1,7\\ & 1,1,1\end{array}$
$\therefore$ LCM of 12, 15 and 21 $=2^2\times 3\times 5\times 7=420$
Now, minimum number of packets of brand A$=\frac{420}{12}=35$
Minimum number of packets of brand B$=\frac{420}{15}=28$
Minimum number of packets of brand C $=\frac{420}{21}=20$