Respuesta :
Answer:
129
Step-by-step explanation:
Let a and b be two numbers.
We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as [tex]GCD(a,b)=3[/tex].
Their least common multiple is twelve times one of the integers. We can represent this information as [tex]LCM(a,b)=12a[/tex].
Now, we will use property [tex]GCD(x,y)*LCM(x,y)=xy[/tex].
Upon substituting our given values, we will get:
[tex]3*12a=ab[/tex]
[tex]36a=ab[/tex]
Switch sides:
[tex]ab=36a[/tex]
[tex]\frac{ab}{a}=\frac{36a}{a}[/tex]
[tex]b=36[/tex]
Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.
The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.
Similarly 96 is also not co-prime with 12 after dividing by 3.
We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.
Let us add 36 and 93 to find the largest possible sum of the required two integers as:
[tex]36+93=129[/tex]
Therefore, the required largest possible sum of the two integers is 129.
