You can check the Church's Deceased Membership File for your Ancestor's membership record  if your family member died between 1941-1988.  This is the record that the Ward Clerk sent into the Church Membership Department when someone in the ward passed away.  This record often tells the parents, children, cause of death, and the Priesthood Ordination dates of male members and who performed the ordinations. 

Not every member's record was turned in.  You must look on a microfilm for the actual record.

At the Church History Library:  On the main floor, East wing, of the Church Office Building, past the security desk (where you will be asked to sign in and show a picture ID), go through the glass doors to your right, then ask at the reference desk and you will be shown the location of the Book where these microfilms are listed.  There are 3 tabs in the book, showing different year ranges--each starts over alphabetically. The records are grouped alphabetically by name ranges, but you have to look on the microfilm to find an individual name.  Example:  John Adams -  Richard Atkinson (roll 1): 

Ask at the reference desk for the microfilms that you wish to view.  There are microfilm reader machines there for you to use.

At the Family History Library:

These microfilms are also available at the Family History Library (you can print this page in order to more easily follow these instructions):

These steps can also be done on your home computer:  At FamilySearch.org website: 

    Click the Library Tab
    Click on Family History Library Catalog
    Click on "Keyword Search"
    Type "deceased members" in the search box, click "search"
    Click on  "Deceased membership records 1941-1988"
    Click on the little box in the upper right hand area that says:  "view film notes"
 
The records are grouped alphabetically by name range, but you have to look on the microfilm to find an individual name.  Example:  John Adams -  Richard Atkinson (roll 1)
It would be nice if each name was listed in the index.

Here's where it gets a little tricky--you have to watch closely.

After Microfilm roll 386, it starts over again alphabetically. Then it starts over alphabetically each year filmed from 1975-1980, then starts over alphabetically for those filmed 1981-1988.  So watch closely to be aware of which alphabetical group you are in.  The latter groups don't list the roll number, but just the microfilm number. 

At the Family History Library:

B1-International Floor  (Basement 1):  Ask at the Service Window for the microfilms you wish to view.  There are microfilm reader machines there for you to you.

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Possible Clue:   One place you can check first that may show you that you will find the name in the Deceased Membership records:

Go to FamilySearch.org and sign on with your username and password so you may see ordinance dates.  Type in the name of your ancestor and do a search of the Internet IGI.  If  records come up for your ancestor, check each record.  Scroll clear to the bottom of the screen on each record and see if there is "source information" listed.  If there is a Batch No. that starts with "H", that indicates that this IGI entry came from the Deceased Membership Records.   If there is a "Source Call No." where there are some numbers shown that are links, this takes you to the "deceased membership records" as the source, then you will know that you should be able to find a copy of the record--probably on one of the microfilm numbers shown.