Question

The fruit vendor sells 18 avocados in one set and 24 kiwis in one set. What is the minimum number of sets of each fruit should Ariana purchase, such that she can distribute the fruits in pairs, having one avocado and one kiwi in each pair?

• A. $3$ sets of avocado.
• B. $4$ sets of kiwi.
• C. $6$ sets of avocado.
• D. $12$ sets of kiwi.

Answer 1

Answer: (A), (B)

$4$ sets of kiwi.

Number of sets of avocado $=18$
Number of sets of kiwi $=24$
As fruits are distributed in pairs, the total number of each fruit type should be equal.

Given number of fruit in each set of both type should be a factor of the total number of fruit of each type that Ariana buys.

To find the minimum set of each fruit, we have to find the LCM of both sets of fruit.

Prime factorisation of $18$ and $24$ is as follows,
$18=2\times 3\times 3$
$24=2\times 2\times 2\times 3$
LCM is $2\times 2\times 2\times 3\times 3=72$

Now, the minimum number of sets of avocado $=\frac{72}{18}=4$
And, the minimum number of sets of kiwi $=\frac{72}{24}=3$