Discussion
Find the smallest number which when divided by 8, 12, and 15 leaves a remainder 5 in each case.
Answer: A
The smallest such number is 125.
A number that leaves remainder 5 when divided by 8, 12 and 15 is 5 more than a common multiple of all three. The smallest is 5 more than their LCM:
\[ \begin{aligned} 8 &= 2^3,\ 12 = 2^2 \times 3,\ 15 = 3 \times 5 \\ \text{LCM} &= 2^3 \times 3 \times 5 = 120 \\ 120 + 5 &= 125 \end{aligned} \]
Check: \(125 = 8 \times 15 + 5 = 12 \times 10 + 5 = 15 \times 8 + 5\). 245, 365 and 485 are 5 more than 240, 360 and 480, which are also multiples of 120, so they leave the same remainder, but they are not the smallest.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development