Math New Drill (Level 2) : Number sense and theory SNJ00-0704-L2 Three integers with 5 of GCD and 450 of LCM

There are three different integers. 

Each of these integers is less than 90 more than 35. 

The Greatest Common Divisor of these three integers is 5 and the Least Common Multiple is 450. 

Find all the groups of these three integers.

Answer
(45, 50, 75), (45, 50, 90), (50, 75, 90)

Solution
Among divisors of 450, look for multiples of 5 which are less than 90 and more than 35. 

The integers applicable to this condition are 45, 50, 75, and 90. 

The combinations of three integers are (45,50,75),(45,50,90),(45,75,90),and (50,75,90). 

Because the Greatest Common Divisor of (45,75,90) becomes 15, this combination should be excluded as it does not apply to the condition.