DURING A DUAL LCL TRAINING FLT; THE FLT INSTRUCTOR PERMITTED THE STUDENT PLT OF A C172 TO FLY OVER A MOUNTAIN PEAK; LOCATED IN A NATIONAL PARK SVC AREA; TO LOOK FOR LOST HIKING FRIENDS. THE ACFT WAS ALLOWED TO CIRCLE AT A LOWER ALT THAN PERMITTED BY THE FOREST SVCS RESTRS.

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I TOOK OFF FROM BJC AROUND XX00 FOR A LCL TRAINING FLT WITH A STUDENT PLT. SHE ASKED IF WE COULD FLY OVER TO LONG'S PEAK; A FEW MI AWAY; TO LOOK AROUND. TWO OF HER FRIENDS HAD GONE ON A 1 DAY CLBING TRIP TO LONG'S PEAK TO PRACTICE ICE CLBING AND HAD BEEN MISSING FOR 3 DAYS. WE FLEW AROUND THE PEAK FROM TIMBERLINE ON UP AND SAW NO ONE UNTIL WE GOT UP TO THE SUMMIT. WE SAW 2 PEOPLE ON TOP AND MADE 3 PASSES TO ASCERTAIN THEIR CONDITION; BEING CAREFUL TO REMAIN 800-1000 FT ABOVE THEM OR AT LEAST 2000 FT LATERAL DISTANCE FROM THEM. ON THE 3RD PASS WE OBSERVED THERE WERE ACTUALLY 3 PEOPLE; ALL STANDING AND MOVING AROUND SO WE FLEW BACK HOME. WHEN WE FIRST SAW THEM ONE OF THEM WAVED BOTH ARMS AT US AS IF TO GET OUR ATTN SO WE WERE AFRAID THEY MIGHT BE HER MISSING FRIENDS AND HAD SOME KIND OF A PROB. WE LATER DISCOVERED THAT LONG'S PEAK IS IN THE ROCKY MOUNTAIN NATIONAL PARK AND WE HAD NOT MAINTAINED 2000 FT OF REQUESTED ALT ABOVE THE TERRAIN. ALSO I FAILED TO CALL FLT SVC AND FIND OUT IF THERE WAS A TEMPORARY RESTR AREA BECAUSE OF THE LOST CLIMBERS; BUT AS FAR AS I'VE FOUND OUT THERE WASN'T. UNKNOWN TO MY STUDENT; OR THE MEDIA; 1 MAN HAD MADE IT DOWN FROM THE SUMMIT AND A RESCUE TEAM HAD RETRIEVED THE OTHER ONE BEFORE WE GOT THERE. THEY'RE BOTH IN THE HOSPITAL WITH FROSTBITE. THE PEOPLE WE SAW AT THE SUMMIT WERE PROBABLY PART OF THE RESCUE TEAM.