The problem solving process is as follows:

12=2×2×3,

16=2×2×2×2,

Because there are fewer than 50 students in this class,

Therefore, the least common multiple of 12 and 16 is: 2× 2× 3× 2× 2 = 48;

There are 48 students in this class.

Extended data:

The solution of the greatest common divisor;

(1) Multiplies the common prime factor by decomposing the prime factor.

(2) Find the greatest common divisor of two numbers in the form of short division.

(3) Special case: If two numbers are coprime, their greatest common divisor is 1.

If the smaller number of two numbers is the divisor of the larger number, then the smaller number is the greatest common divisor of these two numbers.

Least common multiple method;

(1) Multiply these two common prime factors by their unique prime factors by decomposing the prime factors.

(2) In the form of short division.

(3) Special case: If two numbers are prime numbers, then the product of these two numbers is their least common multiple.

If the larger number of two numbers is a multiple of the smaller number, the larger number is the least common multiple of the two numbers.