Question

The product of two numbers is \(8670\) and their HCF is \(17\). What is their LCM?

• A. \(102\)
• B. \(85\)
• C. \(107\)
• D. \(510\)

Hint:

Always remember: \( \text{HCF} \times \text{LCM} = \) product of the two numbers. It saves time when either HCF or LCM is known.

Answer 1

The Correct Option is D

Step 1: Use the relation between HCF, LCM and product.
For two positive integers \(a\) and \(b\):
\[ a \times b = \text{HCF}(a,b) \times \text{LCM}(a,b). \]
Step 2: Substitute the given values and solve for LCM.
\[ 8670 = 17 \times \text{LCM} \;\Rightarrow\; \text{LCM} = \frac{8670}{17} = 510. \]
Step 3: Conclude.
Hence, the LCM is \(510\).