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The least common multiple and the highest common factor of two positive integers are 924 and 12, respectively. How many such unordered pairs are possible?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
yashikaaggarwal
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06 Jul 2022, 09:58
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HCF*LCM = Product of two numbers
12*924 = 12*12*77
The numbers have to be a multiple of 12, the possible pair of numbers can be (12,924) (84,132)
Answer is C
Posted from my mobile device
12*924 = 12*12*77
The numbers have to be a multiple of 12, the possible pair of numbers can be (12,924) (84,132)
Answer is C
Posted from my mobile device
06 Jul 2022, 15:02
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Bunuel
The least common multiple and the highest common factor of two positive integers are 924 and 12, respectively. How many such unordered pairs are possible?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
LCM * HCF = Product of Both Numbers (Both numbers can be expressed as 12a and 12b since their GCD is 12 and a and b are coprime numbers)
924 * 12 = 12a * 12b
ab = 77
Now 77 in prime factorization is 7*11 so product of 77 can only have 2 options (7,11) and (1,77) irrespective of order of elements since that is not important
So the pairs will be 12a and 12b,
Case 1: a=77 and b=1 => (924, 12)
Case 2: a=11 and b=7 => (132, 84)
Answer - C
