The least of five consecutive odd numbers is 2m-1. What is the greatest number?

To find the greatest number among five consecutive odd numbers, we first need to determine the pattern of these numbers. Let's break down the problem step by step:

Step 1: Determine the first odd number:

The least of the five consecutive odd numbers is given as 2m-1. Here, 'm' represents an unknown value. So, the first odd number can be written as 2m-1.

Step 2: Determine the second odd number:

As the numbers are consecutive, the second odd number will be one more than the first odd number. Therefore, the second odd number can be written as (2m-1)+1 = 2m.

Step 3: Determine the third odd number:

Similarly, the third odd number will be one more than the second odd number. So, the third odd number can be written as 2m+1.

Step 4: Determine the fourth odd number:

Following the pattern, the fourth odd number will be one more than the third odd number. Thus, the fourth odd number can be written as (2m+1)+1 = 2m+2.

Step 5: Determine the fifth odd number:

Continuing the pattern, the fifth odd number will be one more than the fourth odd number. Therefore, the fifth odd number can be written as (2m+2)+1 = 2m+3.

Step 6: Finding the greatest number:

To find the greatest number among these five consecutive odd numbers, we compare their values.

The first odd number is 2m-1.
The second odd number is 2m.
The third odd number is 2m+1.
The fourth odd number is 2m+2.
The fifth odd number is 2m+3.

Since these numbers are in increasing order and have different coefficients of 'm', the greatest number will be the one with the highest coefficient of 'm'. In this case, the greatest number is 2m+3.

Therefore, the greatest number among the five consecutive odd numbers is 2m+3.