Let 13 and 273 are the HCF and LCM of two numbers respectively, and if one of…
2024
Let 13 and 273 are the HCF and LCM of two numbers respectively, and if one of them is less than 140 and greater than 60. Then what will be that number?
- A.
121
- B.
91
- C.
75
- D.
131
Attempted by 9 students.
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Correct answer: B
Solution: Let the two numbers be p and q. Given HCF(p, q) = 13 and LCM(p, q) = 273.
Using the product formula p × q = HCF × LCM = 13 × 273 = 13 × 13 × 3 × 7.
Because the HCF is 13, both numbers are multiples of 13. Write p = 13a and q = 13b, where a and b are coprime and satisfy a × b = 273 / 13 = 21.
a = 1, b = 21 → numbers 13 and 273. 13 is less than 60 and 273 is greater than 140, so neither fits the required range.
a = 3, b = 7 → numbers 39 and 91. 39 is less than 60 while 91 lies between 60 and 140, so 91 is the required number.
Answer: 91