Question

Two brands of chocolates, brand A and brand B are available in packs of 24
and 15, respectively. If Rima needs to buy an equal number of chocolates of
both kinds, what is the least number of packs of each kind she needs to buy
respectively?

• A. 5, 8
• B. 8, 5
• C. 5, 4
• D. 10, 8

Answer 1

The correct option is A 5, 8

Number of chocolates in one pack of brand $A=24$
Number of chocolates in one pack brand $B=15$.
From each brand, least number of chocolates to be bought $=LCM$ (24, 15)
LCM by prime factorisation method:
$24=2\times 2\times 2\times 3$
$15=3\times 5$
L.C.M. of 24 and $15=2\times 2\times 2\times 3\times 5=120$
[LCM of two or more numbers = product of the greatest power of each prime factor involved in the prime factorisation of all the numbers]
From each brand, Least number of chocolates to be bought $=120$
Hence, the number of packs of brand $A=\frac{120}{24}=5$
Number of packs of brand $B=\frac{120}{15}=8$