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If two positive integers p and q are written as p=a²b² and q=a³b,a,b are prime numbers, then verify LCM(p,q) × HCF(p,q)=pq

Posted by Jaskaran Kalsi 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Given, p = a²b³
and q = a³b
HCF(p,q) = a²b
LCM(p, q) = a³b³
{tex}\begin{array}{l}pq=a^2b^3\times a^3b=a^5b^4\;-----------(1)\\LCM(p,q)\times HCF(p,q)=a^3b^3\times a^2b=a^5b^4----(2)\\From\;equation\;(1)\;and\;(2)\;We\;get\\LCM(p,q)\times HCF(p,q)\;=\;pq\end{array}{/tex}

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