Find L.C.M from product and H.C.F: The product of two numbers is 1600 and their H.C.F is 5. What is the L.C.M of the two numbers?

Introduction / Context:
The relation a * b = HCF(a, b) * LCM(a, b) allows quick computation of LCM when product and HCF are given. This is a common test of fundamental number theory identities used in aptitude exams.

Given Data / Assumptions:

• a * b = 1600
• HCF(a, b) = 5

Concept / Approach:
Rearrange to LCM = (a * b) / HCF. Because both a and b are integers, the division must be exact and yield an integer LCM.

Step-by-Step Solution:

Verification / Alternative check:
Pick a factor pair of 1600, e.g., 20 and 80, whose HCF is 20 (not 5); but if numbers were 40 and 40, HCF is 40. This shows the specific pair is not needed; the identity already ensures the correct LCM value, independent of the particular pair.

Why Other Options Are Wrong:
1605 and 1595 are near the product and included to trap careless reading; 8000 is product * 5, not product / HCF; 400 does not satisfy the identity with HCF 5.

Common Pitfalls:
Multiplying instead of dividing by HCF; or assuming specific numbers are needed when the identity suffices.

Final Answer:
320