Question : The product of two two-digit numbers is 2160, and their HCF is 12. The numbers are:
Option 1: (12 and 60)
Option 2: (72 and 30)
Option 3: (36 and 60)
Option 4: (60 and 72)
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Correct Answer: (36 and 60)
Solution :
Let the 1st number be $12x$ and the other be $12y$
Given: $HCF =12$ and product of two numbers = 2160
So, product of two numbers = $12x × 12y$
$2160 = 144xy$
$\Rightarrow xy = \frac{2160}{144}$
$\Rightarrow xy = 15$
The possible co-prime pairs of 15 are (1,15) and (3,5)
Therefore, the numbers are (12 $×$ 1 and 12 $×$ 15) or (12 $×$ 3 and 12 $×$ 5)
Hence, the numbers are (12 and 180) or (36 and 60)
Hence, the correct answer is (36 and 60).
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