Correct Answer - Option 3 : 5044
Given:
The number when divided by 21, 28, 36, and 45 and leaves the same remainder 4.
The number is also divisible by 13.
Calculations:
The least number which will be completely divisible by the 21, 28, 36, and 45 will be the LCM of 21, 28, 36, and 45
⇒ LCM(21, 28, 36, 45) = 1260
The least number will be completely divisible by the 21, 28, 36, and 45 and leaves remainder 4 = 1260k + 4
Where,
k = natural number
when k = 1
⇒ 1265
Here 1265 is not divisible by 13.
When k = 1, 2, 3, 4, 5. The number is not divisible by 13.
Now, k = 4
Number = 1260 × 4 + 4
⇒ Number = 5044
The number 5044 is divisible by 13
