I'm not as familiar with momentjs
but this is relatively easy to do in pure Javascript. To get the closest 15 minutes you can use this solution here. Then if you put that in a date variable you can just add 15 minutes as many times as you want! So the resulting Javascript is:
var d = new Date();
var result = "";
for (var idx = 0; idx < 3; idx++)
{
var m = (((d.getMinutes() + 7.5)/15 | 0) * 15) % 60;
var h = ((((d.getMinutes()/105) + .5) | 0) + d.getHours()) % 24;
d = new Date(d.getYear(), d.getMonth(), d.getDay(), h, m, 0, 0);
if (idx > 0) result += ", ";
result += ("0" + h).slice(-2) + ":" + ("0" + m).slice(-2);
d = addMinutes(d, 15);
}
SEE THIS IN A FIDDLE
Notes - I just added 15 minutes 3 times arbitrarily. You could calculate the difference between the time you want and now if you need a different number of intervals. Also note that I don't know exactly what this would do if it is almost midnight, though that would be easy enough to test and code around.
Best of luck!