Problems on LCM & HCF Mcqs

Q.  The product of two numbers is 2028 and their H.C.F is 13. The number of such pairs is__________?

a. 1
b. 2
c. 3
d. 4


ANSWER: See Answer
 
Let the numbers be 13a and 13b.

Then, 13a * 13b = 2028 => ab = 12.
Now, co-primes with product 12 are (1, 12) and (3, 4).
So, the required numbers are (13 * 1, 13 * 12) and (13 * 3, 13 * 4).
Clearly, there are 2 such pairs.
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