Find the pattern in the following examples: a) 8, 12 -> 24; b) 21, 49 -> 147.

$$
8 = 2 \times 2 \times 2 = 2^3
$$
$$
12 = 2 \times 2 \times 3 = 2^2 \times 3^1
$$

The LCM is found by taking the highest power of all prime factors present in either number.
$$
\text{LCM}(8, 12) = 2^3 \times 3^1 = 8 \times 3 = 24
$$
The number in the square is the LCM of the two numbers in the circles.

$$
21 = 3 \times 7
$$
$$
49 = 7 \times 7 = 7^2
$$

$$
\text{LCM}(21, 49) = 3^1 \times 7^2 = 3 \times 49 = 147
$$
The number in the square is indeed the LCM of the two numbers in the circles.