Using L.C.M or H.C.F to determine the time at which two events occur simultaneously again

Question

In an experiment, there are two light bulbs; one is red and one is green. The red light bulb flashes every 20 minutes an the green light bulb flashes every 25 minutes. If the two light bulbs flash at the same time at noon, when will they flash at the same time again?

Answer 1

You need to find the lcm of $20$ and $25$ here as you want the number which comes in tables of both $20$ and $25$ and least with such property i.e. $100$, as $100=25\times 4 =20\times 5$ so both bulbs flash after $1$ hr and $40 $minutes i.e. $1:40 $ pm

Answer 2

Time interval (in minutes) of red bulb $$20=2^2\times 5$$ $$\underbrace{\color{red}{20}, \ \ \ 40\ \ \ \ \ 60\ \ \ \ 80\ \ \ \color{red}{100}}$$ Time interval(in minutes) of green bulb $$25=5^2$$ The time intervals can be represented as follows $$\underbrace{\color{green}{25} \ \ \ \ \ \ \ 50 \ \ \ \ \ \ \ \ \ 75\ \ \ \ \ \color{green}{100}}$$

It is clear that both the bulbs will flash at the same time after 100 minutes which is calculated by taking Least Common multiple of $20$ & $25$ as follows $$LCM(20=2^2\times 5, \ \ 25=5^2)\equiv 2^2\times 5^2=100\ minutes$$
Hence, the bulbs will flash again at the same time after 100 minutes or 1 hour & 40 minutes later i.e. at 1:40 p.m.