ibm - 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 - skillgun

Product of two numbers = product of their HCF and LCM
Product of HCF and LCM = 13 x 273
Since HCF is 13, the number may be 13a and 13b where a and b are co-primes.
Then 13a x 13b = 13 x 273
ab = 13 x 273 / 13 x 13 = 21
The co-primes with product 21 are (1,21) and (7,3)
So, the pair of numbers are (13 x 1, 13 x 21) and (13 x 7 and 13 x 3).
Since one number lies between 60 and 140, the suitable pair (13 x 7 and 13 x 3) = (91, 39)
Hence the required number is 91.