Problem
NT-B1-M02-P012 GCD and LCM with 36
#12
★★☆☆☆ Level 2 of 5
Find positive \(n\) if \(\gcd(n,36)=12\) and \(\operatorname{lcm}(n,36)=180\).
Use the product of the GCD and LCM.
\(36n=12\cdot180\), so \(n=60\). Check: \(\gcd(60,36)=12\), \(\operatorname{lcm}(60,36)=180\). The answer is \(60\).
Another reinforcement of using the formula in reverse.