The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one number is 275, find the other.

Given data

• H.C.F. = 11
• L.C.M. = 7700
• One number = 275

Concept / Approach

• For any two numbers a and b: a × b = HCF × LCM.

Step-by-step calculation

a × b = 11 × 7700 = 84700Other number = 84700 ÷ 275 = 308

Verification

gcd(275, 308) = 11 and lcm(275, 308) = 7700 (since 275×308 = 84700 = 11×7700).

Common pitfalls

• Dividing 7700 by 275 (incorrect method) instead of using product = HCF × LCM.

Final Answer

Other number = 308.