How many numbers between 500 and 900 both inclusive are exactly divisible by all the numbers 12 15 2...........

Quantitative Aptitude (MTS) Number System

How many numbers between 500 and 900, both inclusive,are exactly divisible by all the numbers, 12, 15, 20 and 30?

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SSC MTS 12th October 2021 Shift-2

To solve the problem, we need to find numbers between 500 and 900 divisible by 12, 15, 20, and 30.

- Find the Least Common Multiple (LCM) of the numbers 12, 15, 20, and 30, since a number divisible by all must be divisible by their LCM.

- LCM of 12, 15, 20, and 30 is 60.

- Now, find numbers between 500 and 900 that are divisible by 60.

- First such number is closest multiple of 60 above 500: 540.

- Last such multiple of 60 below 900 is 900 itself.

- Count these multiples: 540, 600, 660, 720, 780, 840, 900.

? Answer: Option:3, 7

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