37 students are standing in a row. Every 4th student is wearing a cap. Every 5th student is wearing a coat. Which students in the row will be wearing both a cap and a coat?

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Solution

Every 4th student is wearing cap i.e. it is divisible by 4.

And every 5th is wearing a coat. i.e. it is divisible by 5.
So, if we want to find out which student is wearing both cap and coat, we need to find the LCM of 4 and 5.

LCM of 4 and 5 = 4 $\times$ 5 = 20. Since they are co-prime numbers, their LCM will be the product of these numbers.

So, 20th student in a row will be wearing both a cap and a coat.

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