Question : The product of the two numbers is 38025 and their highest common factor is 65. What is the least common multiple of these numbers?
Option 1: 455
Option 2: 585
Option 3: 715
Option 4: 435
Correct Answer: 585
Solution :
Let the two numbers be $a$ and $b$.
$a \times b = 38025$
$\text{HCF}(a, b) = 65$
We know, $\text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b$
$\therefore\text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} = \frac{38025}{65} = 585$
Hence, the correct answer is 585.
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