Multiple choice

HCF and LCM of two numbers are 6 and 60 respectively. If the sum of the numbers is 66, what is the larger number?

  1. 12

  2. 30

  3. 45

  4. 60

  5. 90
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D Correct answer
Explanation

Let the numbers be 6a and 6b where a and b are coprime. LCM = 6ab = 60, so ab = 10. Pairs (a,b) are (1,10) and (2,5). Sum = 6(a+b) = 66, so a+b = 11. The pair (1,10) gives sum 11. Numbers are 6*1 = 6 and 6*10 = 60.

AI explanation

Let the two numbers be 6a and 6b where a and b are coprime. Their least common multiple is 6ab, so 6ab = 60, meaning ab = 10. The sum of the numbers is 6a + 6b = 66, meaning a + b = 11. The coprime pairs that multiply to 10 are (1, 10) and the sum of 1 and 10 is 11. The larger number is 6 * 10, which equals 60.

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