What is the largest two digit number which is exactly divisible by both 6 and 5 ?

Options

A. 90
B. 92
C. 60
D. 96

Answer

To find the largest two-digit number that is exactly divisible by both 6 and 5, we can follow these steps:

### Step 1: Find the LCM of 6 and 5
To determine the largest two-digit number that is divisible by both 6 and 5, we first need to find the least common multiple (LCM) of these two numbers.

- The prime factorization of 6 is \(2 \times 3\).
- The prime factorization of 5 is \(5\).

Since there are no common factors, the LCM is calculated by multiplying the highest powers of all prime factors:

\[ LCM(6, 5) = 2^1 \times 3^1 \times 5^1 = 30 \]

### Step 2: Identify the largest two-digit number
The largest two-digit number is 99.

### Step 3: Find the largest two-digit number divisible by 30
To find the largest two-digit number that is divisible by 30, we can divide 99 by 30 and take the integer part of the quotient:

\[ \frac{99}{30} \approx 3.3 \]

Taking the integer part, we have 3. Now, we multiply 3 by 30 to find the largest two-digit number divisible by 30:

\[ 3 \times 30 = 90 \]

### Step 4: Conclusion
Thus, the largest two-digit number that is exactly divisible by both 6 and 5 is **90**.

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