What is the least number which when divided by 18 24 and 36 leaves 3 as a remainder in each case ........

Quantitative Aptitude (MTS) Number System

What is the least number which when divided by 18, 24 and 36 leaves 3 as a remainder in each case?

This questions was previously asked in

SSC MTS 11th July 2022 Shift-3

111

- To solve the problem, we need to find a number that leaves a remainder of 3 when divided by 18, 24, and 36.

- This can be done by first finding the Least Common Multiple (LCM) of the numbers 18, 24, and 36.

- The LCM of 18, 24, and 36 is 72.

- The number we seek is 3 more than a multiple of 72, i.e., in the form of 72k + 3.

Let's evaluate the options:

- Option 1: 75: $$(75-3)/18 = 72/18 = 4,$$ $$(75-3)/24 = 72/24 = 3,$$ $$(75-3)/36 = 72/36 = 2.$$

- Option 2: 93 does not satisfy any.

- Option 3: 111 does not satisfy any.

- Option 4: 99 does not satisfy any.

Thus, Option 1: 75 is the correct answer.

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