#Numbers - 17
The LCM of two numbers "a" and "b" has eight factors. If the sum of these two numbers is 45. Find the maximum product of "a" and "b". Solution- a + b = 45 for product to be maximum, a and b must be as close as possible, => a = 22, b = 23 LCM(a,b) = 22*23 = 506 Factors of 506 = 2*11*23 =>(1+1)*(1+1)*(1+1) = 8 Hence maximum value of the product = 22*23 = 506 ANS