Problem
NT-B1-M02-P003 Product of GCD and LCM
#3
★☆☆☆☆ Level 1 of 5
Let \(a=96\), \(b=180\). Verify \(ab=\gcd(a,b)\operatorname{lcm}(a,b)\).
Find the GCD and LCM by factorisation.
\(96=2^5\cdot3\), \(180=2^2\cdot3^2\cdot5\). Thus \(\gcd=2^2\cdot3=12\), \(\operatorname{lcm}=2^5\cdot3^2\cdot5=1440\). We get \(96\cdot180=17280\) and \(12\cdot1440=17280\).
The formula will be used often in inverse problems.