The product of two whole numbers is 1500 and their highest common factor (HCF) is 10. Find the least common multiple (LCM).

Introduction / Context:This question directly applies the foundational identity for two positive integers: product = HCF * LCM. Given the product and HCF, we can solve immediately for the LCM.

Given Data / Assumptions:

• Product of the two numbers = 1500
• HCF = 10
• Numbers are whole (nonnegative integers)

Concept / Approach:Use the identity: number1 * number2 = HCF * LCM. Rearranging gives LCM = (number1 * number2) / HCF. Substitute the given values.

Step-by-Step Solution:LCM = (product) / HCF = 1500 / 10 = 150.

Verification / Alternative check:If the numbers were, for instance, 30 and 50, their product is 1500 and HCF is 10, giving LCM = 150. This aligns with the computed value and the identity.

Why Other Options Are Wrong:15000 misplaces the division; 1500 and 15 confuse product versus factors; 300 doubles the correct result without basis.

Common Pitfalls:Inverting the formula, or assuming HCF and LCM are themselves the numbers. Always apply product = HCF * LCM carefully.

Final Answer:150