Question

A radio station runs a phone-in contest for listeners. Every ${40}^{th}$ caller gets a free smartphone and every ${60}^{th}$ caller gets a free laptop. Which caller number is the first to receive both the smartphone and the laptop?

Answer 1

The first caller number to win both a smartphone and a laptop has to be a multiple of both 40 and 60 $\Rightarrow$ LCM (40, 60)
Extracting common factors of 40 and 60:

LCM = $2\times 2\times 2\times 3\times 5=120$
Hence, ${120}^{th}$ caller will receive both the smartpone and the laptop.