The smallest number, which when increased by 5 is divisible by each of 24, 32, 36 and 64 is =?

Question: The smallest number, which when increased by 5 is divisible by each of 24, 32, 36 and 64 is =?

Solution:
To find the least common multiple (LCM) of the given numbers (24, 32, 36, 64), we can first find the prime factorization of each number:

24 = 2³ × 3
32 = 2⁵
36 = 2² × 3²
64 = 2⁶

Then, we take the highest power of each prime factor that appears in any of the numbers:
The highest power of 2 is 2⁶
The highest power of 3 is 3²

So, the LCM is 2⁶ × 3² = 64 × 9 = 576

∴ The required number is 576 − 5 = 571