A number theory problem by Kaleem Kħặŋ

flashlight A flashes after--- $20,40,60,80,100$ .....seconds.

flashlight B flashes after -- $25,50,75,100$ ........seconds.

so, they will flash together at after $100$ seconds.

The problem is essentially asking for the lowest common multiple (LCM) of $20$ and $25$ , or equivalently, to find two positive integers $m$ and $n$ such that $20m = 25n$ . To solve this, the most basic method is to make two lists containing the multiples of $20$ and $25$ :

Multiples of $20$ : $20,40,60,80,\color{#3D99F6}{100}$

Multiples of $25$ : $25,50,75,\color{#3D99F6}{100}$

Since $100$ appears in both of the lists, it is a common multiple of both $20$ and $25$ . Therefore, we can select $100$ as the answer.