Let's determine two numbers whose greatest common divisor is 21 and least common multiple is 3969.
Let's write the given numbers in their prime factorization form:

The greatest common divisor: $21=3 \cdot 7$

The least common multiple: $3969=3^{4} \cdot 7^{2}$

The sought pair of numbers $A, B$ can be obtained in two ways:

a) If 3 and 7 appear in the same number to the first power, then in the other number, both prime factors must appear to the highest power they occur.

Thus, $A_{1}=3 \cdot 7=21$ and $B_{1}=3^{4} \cdot 7^{2}=3969$

b) If 3 appears to the first power in one number and 7 appears to the first power in the other, in both cases the co-factors must appear to the highest power they occur, that is,

$$
A_{2}=3 \cdot 7^{2}=147 \quad \text { and } B_{2}=3^{4} \cdot 7=567 \text {. }
$$

Fejes Kálmán (Debrecen, Ref. g. I. o. t.)