Question Number 62554 by Rasheed.Sindhi last updated on 22/Jun/19
$${If}\:{a}\:\&\:{b}\:{are}\:{two}\:{natural}\:{numbers} \\ $$ $${then}\:{the}\:{following}\:{relation}\:{holds} \\ $$ $${always}. \\ $$ $$\:\:\:\:\:{a}×{b}=\mathrm{gcd}\left({a},{b}\right)×\mathrm{lcm}\left({a},{b}\right) \\ $$ $$\:^{\bullet} {If}\:{a},{b}\:\&\:{c}\:\:{are}\:{three}\:{natural}\:{numbers} \\ $$ $$\:\:\:{what}\:{relation}\left({anologous}\:{to}\:{the}\:{above}\right) \\ $$ $$\:\:\:\:{holds}\:{between}\:{numbers}\:{and}\:{their} \\ $$ $$\:\:\:\mathrm{gcd}\:\&\:\mathrm{lcm}? \\ $$