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If two positive integers p and q are written as p = a²b³ and q = a³b ; a, b are prime numbers, then verify : LCM(p, q) *HCF(p, q).

Posted by Aarti Kushwah 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

LCM(p,q) = a³b³
and HCF(p,q) = a²b
LCM(p,q) {tex}\times{/tex} HCF(p,q) = a³b³ {tex}\times{/tex} a²b

{tex}\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}{/tex}

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