Number System

HCF & LCM

Medium

If the HCF of two natural numbers is 12 and the product of the numbers is 2028, how many such pairs exist?

None of these

✅ Correct Option: 3

Since the HCF of the two numbers is 12, both numbers can be written as $12a$ and $12b$ , where $\gcd(a, b) = 1$ .

Using the product condition:

$12a \times 12b = 2028$

$144ab = 2028$

$ab = \dfrac{2028}{144}$

$ab = 14.083...$

Since $a$ and $b$ must be natural numbers, $ab$ must be a whole number. This is not possible here.

No such pair of numbers exists.

The answer is None of these.

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Solution

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