The HCF of two numbers is 12 and their LCM is 72. If one number is 24, find the other.

Explanation

• For any two numbers, first number × second number = HCF × LCM.
• Put in the values: 24 × x = 12 × 72 = 864, so x = 864 ÷ 24 = 36.
• Verify the pair: the HCF of 24 and 36 is 12 and their LCM is 72, so 36 satisfies both conditions.
• Option A 24 is wrong because the HCF of 24 and 24 would be 24, not 12.
• This rule holds only for two numbers. For three or more numbers the product of the HCF and LCM is not equal to the product of the numbers.
• HCF and LCM questions appear often in NTS and PPSC maths sections, and this single formula solves most of them.