Question : If $x : y$ is the ratio of two whole numbers and $z$ is their HCF, then the LCM of those two numbers is:
Option 1: $yz$
Option 2: $\frac{xz}{y}$
Option 3: $\frac{xy}{z}$
Option 4: $xyz$
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Correct Answer: $xyz$
Solution :
Given: The ratio of number = $x : y$
Highest Common Factor = $z$
Here, $z$ is the common factor of $x$ and $y$. So, the numbers will be $xz$ and $yz$.
Now, $xz × yz$ = Highest Common Factor(HCF) × Lowest Common Multiple(LCM)
So, the Lowest Common Multiple(LCM) = $\frac{xz × yz}{z}$ = $xyz$
Hence, the correct answer is $xyz$.
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