Question 138
Let $[x_1, x_2]$ and $[y_1, y_2, y_3]$ be the least common multiple of $x_1, x_2$ and $y_1, y_2, y_3$ respectively. For any positive integers $a, b, c, d$ let $A$ and $B$ be such that:
$$
A = [a, b, c] \cdot [a, b, d] \cdot [a, c, d] \cdot [b, c, d] \text{ and } B = [a, b] \cdot [a, c] \cdot [a, d] \cdot [b, c] \cdot [b, d] \cdot [c, d].
$$
Show that $A^6 \geq B^4$.
$$
A = [a, b, c] \cdot [a, b, d] \cdot [a, c, d] \cdot [b, c, d] \text{ and } B = [a, b] \cdot [a, c] \cdot [a, d] \cdot [b, c] \cdot [b, d] \cdot [c, d].
$$
Show that $A^6 \geq B^4$.