Both 12 and 60 are superior highly composite numbers^[1] which makes mental math easy. 60 in particular is a very nice number because it has 12 divisors and is the smallest number divisible by all the numbers 1 through 6.
Nah. Just start counting on your fingers. 123 on the index, 456 on the middle, 789 on the ring, and the rest on your pinkie. Its based on the segments of each finger, and it's how Mayans used to count.