The HCF of two numbers is 18 and their sum is 162. What is their LCM?

Solution

 Let the two numbers be x and y. We know that their HCF is 18, which means that both x and y are multiples of 18.  Let x = 18a and y = 18b,  where a and b are integers.  We also know that x + y = 162.  Substituting the values of x and y,  we get 18a + 18b = 162, or a + b = 9.  We can say that according to the option  If a = 5 and b = 4  Then we can say that numbers will be  18 x 5 = 90 and 18 x 4 = 72  So the LCM of the numbers will be  LCM of 90 and 72 is 360.