Question : The HCF and LCM of the two numbers are 21 and 84, respectively. If the ratio of the two numbers is 1:4, then the larger of the two numbers is:
Option 1: 12
Option 2: 108
Option 3: 48
Option 4: 84
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Correct Answer: 84
Solution : Given: The ratio of the two numbers is 1:4 and the Highest Common Factor (HCF) is 21. Here, the common factor is 21. Let the numbers be k and 4k k × 4k = 21 × 84 k 2 = 21 × 21 ⇒ k = 21 So, numbers will be 1 × 21 = 21 and 4 × 21 = 84 84 is larger than 21. Hence, the correct answer is 84.
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