Briggs & Stratton's #1 choice in motor oil is synthetic 5W30, which they sell under their own brand name. They also sell and recommend straight 30 weight for use above 40 degrees. They recommend 5W30 synthetic from -20 degrees to +120 degrees. They go on to say that dino multigrade oils may cause consumption if used above 80 degrees.
Their 5W30 synthetic is not the new API SM grade. I have been using Mobil 1 5W30 in my Honda engined mower since I bought it back in 2000. I used the last of my old stock Mobil 1 which was not SM this year. I have bought a supply of Mobil 1 High Mileage 10W30, which is SL, and not SM rated. Inasmuch as Honda calls for any kind of 10W30 motor oil, my mower should like it just fine.