Question

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, then what is the minimum number of packets of each brand he should buy? [4 MARKS]

Answer 1

Formula: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

For a minimum number of biscuits, first, we find the LCM of 12, 15 and 21.
The prime factors of the following numbers are:
12=2$\times$2$\times$3
15=3$\times$5
21=3$\times$7
The maximum number of times the prime factor 2 occurs is 2.
The maximum number of times the prime factor 3 occurs is 1.
The maximum number of times the prime factor 5 occurs is 1.
The maximum number of times the prime factor 7 occurs is 1.
$\therefore$ LCM= 3 $\times$ 4 $\times$ 5 $\times$ 7 = 420
$\therefore$ Minimum number of packets of brand A $=\frac{420}{12}=35$
Minimum number of packets of brand B $=\frac{420}{15}=28$
And minimum number of packets of brand C $=\frac{420}{21}=20$