Question : The HCF and LCM of the two numbers are 126 and 9 respectively. If one of the numbers is 18, then what is the other number?
Option 1: 63
Option 2: 36
Option 3: 84
Option 4: 24
Correct Answer: 63
Solution : The product of two numbers is equal to the product of their HCF (Highest Common Factor) and LCM (Least Common Multiple). Let the two numbers as a and b, with a = 18 (given). The HCF is 126 and the LCM is 9. ⇒ a × b = HCF × LCM ⇒ 18 × b = 126 × 9 ⇒ b = 63 Hence, the correct answer is 63.
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Question : The HCF and LCM of two numbers are 9 and 126, respectively. Find the larger number, if the ratio between the numbers is 2 : 7.
Option 1: 42
Option 2: 63
Option 3: 77
Option 4: 21
Question : The LCM of the two numbers is 44 times their HCF. The sum of the LCM and HCF is 1125. If one number is 25, then the other number is:
Option 1: 1100
Option 2: 975
Option 3: 900
Option 4: 800
Question : The LCM of two numbers is five times their HCF. If the product of the two numbers is 20480, then find their HCF and LCM, respectively.
Option 1: 46 and 230
Option 2: 48 and 240
Option 3: 64 and 320
Option 4: 56 and 280
Question : The LCM of the two numbers is 840 and their HCF is 7. If one of the numbers is 56, find the other.
Option 1: 120
Option 2: 112
Option 3: 105
Option 4: 84
Question : The HCF and the LCM of two numbers are 5 and 175, respectively. If the ratio of the two numbers is 5 : 7, the larger of the two numbers is _______.
Option 1: 35
Option 2: 25
Option 3: 45
Option 4: 75
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