Problem
NT-B1-M02-P007 Recover the Number
#7
★★☆☆☆ Level 2 of 5
Find positive \(n\) if \(\gcd(n,90)=18\) and \(\operatorname{lcm}(n,90)=630\).
Use \(90n=\gcd(n,90)\operatorname{lcm}(n,90)\).
We have \(90n=18\cdot630\), so \(n=126\). Check: \(\gcd(126,90)=18\), \(\operatorname{lcm}(126,90)=630\), so the answer is correct.
Always check: the formula gives a candidate, but the GCD condition must still be confirmed.