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If p,q are two positive integer written as p=a.a.b.b.b and q=a.a.a.b ;a,b are prime number then verify : LCM(p,q) *HCF(p,q)=pq

Posted by Ankit King 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

LCM(p,q) = a³b³
and HCF(p,q) = a²b
LCM(p,q) $\times$ HCF(p,q) = a³b³ $\times$ a²b

$\begin{array}{l}\mathrm{LCM}(\mathrm p,\mathrm q)\;\times\mathrm{HCF}(\mathrm p,\mathrm q)\;=\mathrm a^5\mathrm b^4\;-----(1)\\\mathrm{and}\;\mathrm{pq}=\mathrm a^2\mathrm b^3\;\times\mathrm a^3\mathrm b=\mathrm a^5\mathrm b^4\;------(2)\\\mathrm{from}\;\mathrm{eq}^\mathrm n\;(1)\;\mathrm{and}\;(2)\\\mathrm{LCM}(\mathrm p,\mathrm q)\;\times\mathrm{HCF}(\mathrm p,\mathrm q)\;\;=\mathrm{pq}\\\\\end{array}$

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