Question

Given that HCF(255, 867) = 51, find the value of LCM(255, 867).

Hint:

To find the LCM of two numbers, use the relationship \( \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \).

Answer 1

We know the relationship between HCF and LCM for two numbers \( a \) and \( b \) is given by: \[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b. \] Given that: - \( \text{HCF}(255, 867) = 51 \), - \( a = 255 \), - \( b = 867 \). Substitute the values into the formula: \[ 51 \times \text{LCM}(255, 867) = 255 \times 867. \] Calculate \( 255 \times 867 \): \[ 255 \times 867 = 221085. \] Now, solve for LCM: \[ \text{LCM}(255, 867) = \frac{221085}{51} = 4335. \]
Conclusion: The value of \( \text{LCM}(255, 867) \) is \( 4335 \).