Question

Find the LCM of 867 and 255.
 

Hint:

Always apply Euclid’s Division Lemma step-by-step to find HCF, then use the relation \(\text{LCM} \times \text{HCF} = a \times b\).

Answer 1

Step 1: Find HCF using Euclid’s algorithm.
\[ 867 = 255 \times 3 + 102 \] \[ 255 = 102 \times 2 + 51 \] \[ 102 = 51 \times 2 + 0 \] Thus, \(\text{HCF} = 51\).
Step 2: Use the relation between HCF and LCM.
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \] \[ 51 \times \text{LCM} = 867 \times 255 \] \[ \text{LCM} = \frac{867 \times 255}{51} = 4335 \]
Step 3: Conclusion.
\[ \boxed{\text{HCF} = 51, \quad \text{LCM} = 4335} \]