Let x be the least number which on being divided by 8 12 15 24 25 and 40 leaves a remainder of 7 in ...........

Quantitative Aptitude (MTS) Number System

Let x be the least number which on being divided by 8, 12, 15, 24, 25 and 40 leaves a remainder of 7 in each case. What will be

the remainder when x is divided by 29?

This questions was previously asked in

SSC MTS 6th October 2021 Shift-2

- The least number \( x \) which, when divided by 8, 12, 15, 24, 25, and 40, leaves a remainder of 7 is of the form:

\( x = \text{LCM}(8,12,15,24,25,40) + 7 \).

- Let's find the LCM:

- 8 = 2³

- 12 = 2² × 3

- 15 = 3 × 5

- 24 = 2³ × 3

- 25 = 5²

- 40 = 2³ × 5

- Highest powers: 2³, 3¹, 5²

- LCM = 2³ × 3¹ × 5² = 8 × 3 × 25 = 600.

- So, \( x = 600 + 7 = 607 \).

- To find remainder when 607 is divided by 29:

- 29 × 20 = 580, 607 - 580 = 27.

- So, remainder is 27.

- Option 1: 18?? ?

- Option 2: 27

- Option 3: 19?? ?

- Option 4: 20?? ?

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