If the HCF of two numbers is one of the numbers, then their LCM is the other number.
Step 1: Let the two numbers be \(a\) and \(b\) with \(a \le b\).
Step 2: “HCF is one of the numbers” means the bigger number is a multiple of the smaller number. So we can write: \(b = k\,a\) for some whole number \(k\ge 1\).
Step 3: In this situation, the highest common factor is the smaller number: \(\text{HCF}(a,b) = a\). (Because every divisor of \(b\) that is also a divisor of \(a\) cannot be bigger than \(a\), and \(a\) itself divides \(b\).)
Step 4: The common multiples of \(a\) and \(b\) are multiples of \(b\) (since \(b\) already contains \(a\) as a factor). The smallest such multiple is \(b\) itself. So \(\text{LCM}(a,b) = b\).
Step 5 (quick check using a formula): We know \(a\times b = \text{HCF}(a,b)\times \text{LCM}(a,b)\). If \(\text{HCF}(a,b)=a\), then \(a\times b = a\times \text{LCM}(a,b)\) ⇒ \(\text{LCM}(a,b)=b\).
Therefore, if the HCF is one of the numbers (say \(a\)), the LCM is the other number (\(b\)).