#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
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
Just wow.
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