The least squares mean is different from the sample mean. JMP Or simply from other statistical software. However, to calculate this manually, you need to take the following steps.
For example, we used Big Class.jmp file, which is JMP Sample Data Table. We will change the Age variable to Continuous to meet the purpose of obtaining LS Mean.

Assuming that the LS Means Table is obtained using Big Class, jmp data, the LSMean values of categorical variables sex are 107.32515 for F and 103.09760 for M, respectively.
To find the LSMean of a categorical variable, we need a sample mean of a continuous variable (where Age and Height are the sample mean, see JMP Output below), and also an estimate from the above output.

In order to understand the manual work more easily, I have used Excel. In the screenshot below, we can see that LSMean is obtained by using the sample mean of each continuous variable in the estimation formula. In other words, you can get it easily by applying +1 for Female and -1 for Male.

Please refer to the attached Excel file for the actual formula.
In addition, see the link below for a description of LS Mean.
LSMeans Table