Two numbers are in the ratio 3 : 4 and their HCF is 4. What is their LCM?

Introduction:
If two numbers are 3k and 4k and their highest common factor is k, then using the product relation HCF * LCM = product of the numbers gives the LCM directly.

Given Data / Assumptions:

• Numbers in ratio 3 : 4
• HCF = 4

Concept / Approach:
Let the numbers be 3k and 4k with HCF = k. Given k = 4, so numbers are 12 and 16. Then LCM = (12 * 16) / HCF(12, 16) or more simply LCM = product / HCF.

Step-by-Step Solution:

Verification / Alternative check:
Multiples of 16 that are also multiples of 12: 48 is the least such value.

Why Other Options Are Wrong:
12 and 16 are too small, 24 is a multiple of 12 but not 16, and 64 is larger than necessary.

Common Pitfalls:
Confusing HCF with the common multiplier k in the ratio without following through to actual numbers.

Final Answer:
48