Two numbers are in the ratio \(x : y\), where \(x\) and \(y\) are co-prime, and their HCF is \(z\). What is their LCM?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(xyz\)
When the ratio \(x : y\) is in its lowest terms, the HCF \(z\) is the common part of both numbers, so the numbers are \(xz\) and \(yz\). The LCM keeps the common part once and both remaining parts.
Numbers: \(xz\) and \(yz\)
\(x\) and \(y\) have no common factor, so the LCM \(=z\times x\times y\)
LCM \(=xyz\)
The LCM is \(xyz\). The same follows from HCF \(\times\) LCM \(=\) product of the numbers: \(z\times xyz=xz\times yz\).