Correct Answer - Option 2 : 293
Given:
The largest number between 200 and 300 should be divisible by 6, 8 and 9 and in each case leave a remainder 5
Concept Used:
⋆ LCM (Least Common Multiple): LCM of x and y is the least common multiple of x and y which is perfectly divisible by both x and y
For Example,
3 → Multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, …
4 → Multiple of 4 are 4, 8, 12, 16, 20, 24, 28, 32, …
Here common are 12 and 24. But of these 12 is least
∴ LCM of 3 and 4 is 12
⋆ When the remainder will be same in each case, the number should be LCM of all those divisor + remainder
Calculation:
The number should be divisible by 6, 8 and 9
LCM of 6, 8, 9 is 72
Now, we have to find the largest number between 200 and 300 which will be divisible by 72
72 × 1 = 72
72 × 2 = 144
72 × 3 = 216
72 × 4 = 288
72 × 5 = 360
From the above 216 and 288 are between 200 and 300 which will be divisible by 72
From these two 288 is larger which is divisible by 72, i.e. divisible by 6, 8 and 9
In all cases, the remainder is 5
The required number is 288 + 5
⇒ 293
∴ The largest number between 200 and 300 is 293 which when divided by 6, 8 and 9 leaves a remainder 5 in every case.
