Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?
Given:
Number of chocolates in a pack of 1st brand = 24
Number of chocolates in a pack of 2nd brand = 15
To find: Here we have to find the least number of boxes of each kind need to buy to get an equal number of chocolates of both kinds.
Solution:
To find the least number of boxes to buy an equal number of chocolates we need to calculate the LCM of 24 and 15.
Calculating LCM of 24 and 15:
Writing the numbers as a product of their prime factors:
Prime factorization of 24:
- $2\ \times\ 2\ \times\ 2\ \times\ 3\ =\ 2^3\ \times\ 3^1$
Prime factorization of 15:
- $3\ \times\ 5\ =\ 3^1\ \times\ 5^1$
Multiplying the highest power of each prime number:
- $2^3\ \times\ 3^1\ \times\ 5^1\ =\ 120$
So,
LCM(24, 15) $=$ 120
Therefore,
Number of packets of 1st brand $=\ \frac{120}{24}\ =$ 5
Number of packets of 2nd brand $=\ \frac{120}{15}\ =$ 8
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