Find the LCM of two numbers using gcd-lcm relation Compute the least common multiple (LCM) of 87 and 145 efficiently.

Introduction / Context:The fastest way to find the LCM of two numbers is to use the identity LCM(a, b) * gcd(a, b) = a * b. This avoids full prime factorisation if you can quickly see a common factor.

Given Data / Assumptions:

• a = 87, b = 145.
• gcd(87, 145) is needed.

Concept / Approach:Factor lightly: 87 = 3 * 29; 145 = 5 * 29. Their gcd is 29. Then LCM = (87 * 145) / 29.

Step-by-Step Solution:gcd(87, 145) = 29.LCM = (87 * 145) / 29 = 87 * 5 = 435.

Verification / Alternative check:435 ÷ 87 = 5 and 435 ÷ 145 = 3, both integers. No smaller positive number is a multiple of both 87 and 145.

Why Other Options Are Wrong:870 and 1740 are multiples but not the least; 1305 is 435 * 3; 2610 is 435 * 6. Only 435 is the minimal common multiple.

Common Pitfalls:Missing the shared factor 29; multiplying the numbers without dividing by the gcd; mixing up HCF and LCM definitions.

Final Answer:435