Question

Three brands $\mathrm{A},\mathrm{B}$and $\mathrm{C}$ of biscuits are available in pack 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

Step - $1$- : The minimum number of packets of each brand that the shopkeeper should buy, is equal to the LCM.

$12=2\times 2\times 3$

$15=3\times 5$

$21=3\times 7$

L.C.M $(12,15,21)=2\times 2\times 3\times 5\times 7=420$

Step - $2$ -: To find the minimum number of packets we should divide the LCM by the number of biscuits in each packet.

The minimum number of packets of brand A $=\frac{420}{12}=35$
The minimum number of packets of brand B $=\frac{420}{15}=28$
The minimum number of packets of brand C $=\frac{420}{21}=20$

Hence, the minimum number of packets of brands A, B, and C are $35,28,$ and $20$ respectively.