I have a doubt. Feel free to share your ideas. Thanks.

Consider the question: "The name of 'Modern Food Stores' is displayed on a board at a junction using neon lights. When the board is switched on, the lights in each word follow a cyclic pattern of turning on and off. The first word remains lighted for 7/4 seconds and then remains switched off for 2 seconds. The second word remains switched on for 11/3 seconds and then remains switched off for 2 seconds. The third word remains switched on for 15/2 seconds and then remains switched off for 2 seconds. If the board is switched on, what is the smallest interval, after which the entire display will again turn on simultaneously?"

The solution for the question is calculating the LCM of total period ( Ton + Toff) of all the switches and that's the answer. Let's consider a case where there are only two switches and respective Ton of the switches are 1 and 2 and Toff of the switches are 2 and 2. Now, if the same LCM technique is used for solving the question, it doesn't work. Why is that so?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$