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.

To find the maximum value of $A + B$ given the conditions in the passage, we need to follow these steps:

1. Understand the conditions:

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

2. Identify possible values for $B$:

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

3. List the possible values of $B$:

   • Start with $k = 1$: $B = 6(1) + 2 = 8$ (not a 2-digit number)
   • $k = 2$: $B = 6(2) + 2 = 14$
   • $k = 3$: $B = 6(3) + 2 = 20$
   • Continue this process until $B$ exceeds 99:
     • $B = 26, 32, 38, 44, 50, 56, 62, 68, 74, 80, 86, 92, 98$

4. Check the LCM condition for each $B$:

   • The LCM of $A$ and $B$ is 60. We need to find pairs $(A, B)$ such that their LCM is 60.
   • For each $B$, find the corresponding $A$ such that $\text{LCM}(A, B) = 60$.

5. Calculate $A$ for each $B$:

   • Use the formula for LCM: $\text{LCM}(A, B) = \frac{A \times B}{\text{GCD}(A, B)}$.
   • For each $B$, find $A$ such that $\frac{A \times B}{\text{GCD}(A, B)} = 60$.

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

   • Check each valid pair $(A, B)$ and calculate $A + B$.
   • Identify the maximum value of $A + B$.

Let's go through the calculations for each $B$:

• For $B = 14$:

  • $\text{LCM}(A, 14) = 60$
  • Possible $A$ values: 30 (since $\text{LCM}(30, 14) = 60$)
  • $A + B = 30 + 14 = 44$

• For $B = 20$:

  • $\text{LCM}(A, 20) = 60$
  • Possible $A$ values: 15 (since $\text{LCM}(15, 20) = 60$)
  • $A + B = 15 + 20 = 35$

• For $B = 26$:

  • $\text{LCM}(A, 26) = 60$
  • No valid $A$ (since 26 is not a factor of 60)

• For $B = 32$:

  • $\text{LCM}(A, 32) = 60$
  • No valid $A$ (since 32 is not a factor of 60)

• For $B = 38$:

  • $\text{LCM}(A, 38) = 60$
  • No valid $A$ (since 38 is not a factor of 60)

• For $B = 44$:

  • $\text{LCM}(A, 44) = 60$
  • No valid $A$ (since 44 is not a factor of 60)

• For $B = 50$:

  • $\text{LCM}(A, 50) = 60$
  • Possible $A$ values: 6 (since $\text{LCM}(6, 50) = 60$)
  • $A + B = 6 + 50 = 56$

• For $B = 56$:

  • $\text{LCM}(A, 56) = 60$
  • No valid $A$ (since 56 is not a factor of 60)

• For $B = 62$:

  • $\text{LCM}(A, 62) = 60$
  • No valid $A$ (since 62 is not a factor of 60)

• For $B = 68$:

  • $\text{LCM}(A, 68) = 60$
  • No valid $A$ (since 68 is not a factor of 60)

• For $B = 74$:

  • $\text{LCM}(A, 74) = 60$
  • No valid $A$ (since 74 is not a factor of 60)

• For $B = 80$:

  • $\text{LCM}(A, 80) = 60$
  • No valid $A$ (since 80 is not a factor of 60)

• For $B = 86$:

  • $\text{LCM}(A, 86) = 60$
  • No valid $A$ (since 86 is not a factor of 60)

• For $B = 92$:

  • $\text{LCM}(A, 92) = 60$
  • No valid $A$ (since 92 is not a factor of 60)

• For $B = 98$:

  • $\text{LCM}(A, 98) = 60$
  • No valid $A$ (since 98 is not a factor of 60)

From the valid pairs, the maximum value of $A + B$ is $56$ when $A = 6$ and $B = 50$.

Answer: The maximum value of $A + B$ is 56.