Question

The LCM of the smallest 2-digit number and the smallest 3-digit number is expressed in the form 2^p . 5^q. The respective values of p and q are:

Options

• 1, 2

• 1, 1

• 2, 1

• 2, 2

Answer 1

2, 2

Explanation:

1. Identify the numbers

The smallest 2-digit number is 10.

The smallest 3-digit number is 100.

2. Find the Least Common Multiple (LCM)

We need to find the LCM of 10 and 100. Since 100 is a multiple of 10 (10 × 10 = 100), the LCM is simply the larger number:

LCM (10, 100) = 100

3. Express the LCM in the form 2^p . 5^q

Now, we perform prime factorization on 100:

100 = 10 × 10

100 = (2 × 5) × (2 × 5)

100 = 2² . 5²

4. Determine p and q

By comparing 2² . 5² with the given form 2^p . 5^q, we get

p = 2

q = 2

Therefore, the respective values of p and q are 2, 2.