How many integers between 4000 and 6000 are divisible by 32, 40, 48, and 60?

Introduction:
An integer divisible by multiple numbers must be a multiple of their least common multiple. We count how many multiples of that LCM lie in the specified interval.

Given Data / Assumptions:

• Range: 4000 to 6000 inclusive
• Divisors: 32, 40, 48, 60

Concept / Approach:
Compute LCM(32, 40, 48, 60). Then count multiples in the range using ceiling and floor division.

Step-by-Step Solution:

Verification / Alternative check:
Each listed value is divisible by all four divisors by construction through the LCM.

Why Other Options Are Wrong:
2, 3, and 5 do not match the exact count of LCM multiples in the interval.

Common Pitfalls:
Taking pairwise divisibility instead of using the LCM, which can overcount or undercount.

Final Answer:
4