If you Know the cap rate is there a way to calculate the GRM

You divide the price of the real estate by the gross income. ($1,000,000 purchase price/$100,000 gross annual income = 10x gross.

The short answer is yes, and no. Or perhaps more precisely: it depends.
By GRM, I am assuming that you are referring to Gross Rent Multiplier. There is also an effective gross rent multiplier (EGRM); and a Net Income Multiplier.
Traditionally, GRM is calculated by dividing the sales price by the annual Gross Rent, though it can also be done by using monthly rent as opposed to annual rent. It doesn't matter, as long as everyone is on the same page as far as the methodology and terminology.
Accordingly, directly, the cap rate, or the Overall Capitalization Rate, to be more precise, is not used to determine the Gross Rent Multiplier. Thus, technically speaking, if you know only the Cap Rate you can not determine the GRM.
You need the Gross Rent amount and the sales price. If you have the information to calculate the Net Operating Income, and the sales price, then you could calculate the Gross Rent Multiplier.
Simply put, GRM is the sales price divided by the Gross rent. I often look at it as a "shorthand" methodology for doing a quick analysis of a property when the only reliable information that I have handy is the gross rent, and the sales price. In the past, I have found it particularly useful when analyzing small to medium-size apartment complexes, but it can be an effective methodology for larger properties, and for other types of commercial real estate as well.
It is not particularly useful for properties with complex income streams, nor when there are significant variances in the expenses from one property to the next. To be accurate, when applying a gross rent multiplier derived from one property as an evaluation tool, there has to be uniformity with respect to the expense ratios of the two, or more, properties.

In short... no.
To calculate the GRM you must know the annual gross rent. Since you know the cap rate you could back into the NRM (net rent multiplier) but I'm not sure there is such a thing, ha ha.

Dave...
If you know the cap-rate, you very likely know how the cap-rate was calculated. If so, then you know the gross income which is where cap-rate calculations begin. If you indeed know the gross income, then Jackson's answer can then be used.
In commercial real estate, while it has always been interesting for me to compare GRM, it has not been essential to use this calculation. The one that is essential is the cap-rate; and to know how to properly use the rate so that you will not be fooled into paying too much for an asset.
Some of the points that will lead you astray are:
1. Condition of comparable properties and cap rates.
2. Location of comparable properties and cap rates.
3. Inordinate rental rates. (Can these be maintained compared to market rates)?
3. In NNN properties, vacancy rates, as the amount of money that a buyer may have to contribute monthly to expenses until vacant space is leased may indeed add to an overall purchase price.
4. And the biggest question of all. Is the cap rate on a property based on actual income? (To base it on projected income is an amateur's trick, (albeit, an easy trick to spot!)
Good luck and Onward and Upward.....
Rob Baird
rob@capratecommercial.com

Purchase Price: $10M
Cap Rate: 7%
Expenses $150k
NRM = $10M x .07 = $700,000
GRM = $10M/$850,000 = 11.76

NO! Unless undisclosed facts are given or known. Cap rates are often given in reports by top firms such as Korpacz, etc. In small towns where information is limited from the market, the most accurate cap rates are derived by Ellwood through the banking industry while in cities, the most accurate information comes from market transactions.