If two positive integers $p$ and $q$ can be expressed as $p=18 a^{2} b^{4}$ and $q=20 a^{3} b^{2}$,

Question

If two positive integers $p$ and $q$ can be expressed as $p=18 a^{2} b^{4}$ and $q=20 a^{3} b^{2}$, where $a$ and $b$ are prime numbers, then $\operatorname{LCM}(p, q)$ is :\

Professor PC Thomas Classes · Answer

(d): We have,\ $p=18 a^{2} b^{4}=2 	imes 3 	imes 3 	imes a 	imes a 	imes b 	imes b 	imes b 	imes b$\ $q=20 a^{3} b^{2}=2 	imes 2 	imes 5 	imes a 	imes a 	imes a 	imes b 	imes b$\ $	herefore \quad \operatorname{LCM}(p, q)=2 	imes 2 	imes 3 	imes 3 	imes 5 	imes a 	imes a 	imes a 	imes b 	imes b 	imes b 	imes b =180 a^{3} b^{4}$\