PASSAGEDirections Read the given passage carefully and find the answers of following questions. LCM of two numbers A and B is 60. B is a 2-digit number which leaves remainder as 2 when divided by 6. It is also given B>A.Read the instructions carefullyFind Maximum value of A+B.OPTIONS23323550

To solve this problem, we need to follow these steps:

1. Understand the given information:

   • The Least Common Multiple (LCM) of two numbers $A$ and $B$ is 60.
   • $B$ is a 2-digit number that leaves a remainder of 2 when divided by 6.
   • $B$ is greater than $A$.

2. Identify possible values for $B$:

   • Since $B$ leaves a remainder of 2 when divided by 6, $B$ can be written as $B = 6k + 2$ where $k$ is an integer.
   • $B$ is a 2-digit number, so $10 \leq B \leq 99$.

3. List the possible values of $B$:

   • We need to find values of $B$ that fit the form $6k + 2$ and are within the range of 10 to 99.
   • Possible values of $B$ are: 14, 20, 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 92, 98.

4. Determine the corresponding values of $A$:

   • Since the LCM of $A$ and $B$ is 60, $A$ must be a factor of 60.
   • The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.

5. Check each possible $B$ to find the corresponding $A$:

   • For each $B$, we need to check if there is a factor $A$ such that the LCM of $A$ and $B$ is 60 and $B > A$.

6. Calculate the maximum value of $A + B$:

   • We need to find the pair $(A, B)$ that satisfies the conditions and gives the maximum sum $A + B$.

Let's go through the possible values of $B$ and find the corresponding $A$:

• For $B = 14$:

  • The factors of 60 that are less than 14 are: 1, 2, 3, 4, 5, 6, 10, 12.
  • Check if the LCM of each factor with 14 is 60:
    • LCM(10, 14) = 70 (not 60)
    • LCM(12, 14) = 84 (not 60)
    • LCM(6, 14) = 42 (not 60)
    • LCM(5, 14) = 70 (not 60)
    • LCM(4, 14) = 28 (not 60)
    • LCM(3, 14) = 42 (not 60)
    • LCM(2, 14) = 14 (not 60)
    • LCM(1, 14) = 14 (not 60)
  • No valid $A$ for $B = 14$.

• For $B = 20$:

  • The factors of 60 that are less than 20 are: 1, 2, 3, 4, 5, 6, 10, 12, 15.
  • Check if the LCM of each factor with 20 is 60:
    • LCM(15, 20) = 60 (valid pair)
  • $A = 15$, $B = 20$, $A + B = 35$.

• For $B = 26$:

  • The factors of 60 that are less than 26 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20.
  • Check if the LCM of each factor with 26 is 60:
    • No valid $A$ for $B = 26$.

• Continue this process for other values of $B$.

After checking all possible values, we find that the maximum value of $A + B$ is achieved with $B = 20$ and $A = 15$, giving $A + B = 35$.

Therefore, the maximum value of $A + B$ is 35.

Answer: 35