Question

If the product of two numbers is 2880 and their H.C.F. is 12, then the value of their L.C.M. is:

• A. 200
• B. 240
• C. 300
• D. 360

Hint:

Remember, the product of two numbers is equal to the product of their HCF and LCM.

Answer 1

The Correct Option is B

We know that: \[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \] Let the two numbers be \( a \) and \( b \). We are given: \[ a \times b = 2880 \quad \text{and} \quad \text{HCF}(a, b) = 12 \] Using the formula for the product of two numbers, we have: \[ 2880 = 12 \times \text{LCM}(a, b) \] Now, solving for LCM: \[ \text{LCM}(a, b) = \frac{2880}{12} = 240 \]
Step 2: Conclusion.
Therefore, the value of the LCM is 240. Final Answer:} 240.