∵gcd(p,q)≤min(p,q)≤max(p,q)≤lcm(p,q)\because\gcd(p,q)\leq \min(p,q)\leq \max(p,q)\leq \operatorname{lcm}(p,q)∵gcd(p,q)≤min(p,q)≤max(p,q)≤lcm(p,q)
∴max(p,q)min(p,q)≤lcm(p,q)gcd(p,q)\therefore\frac{\max(p,q)}{\min(p,q)}\leq \frac{\operatorname{lcm}(p,q)}{\gcd(p,q)}∴min(p,q)max(p,q)≤gcd(p,q)lcm(p,q)
