Question

what is the LCM and hcf of reciprocal of 18 and 24​

Answer 1

$Given \: numbers : 18 \: and \: 24$

$Reciprocal \: of \: 18 \: is \: \frac{1}{18} \\Reciprocal \: of \: 24 \: is \: \frac{1}{24}$

$LCM \: of \: (18,24) = 72$

$HCF \: of \: (18,24) = 6$

$i ) LCM \:of \: \left( \frac{1}{18}, \frac{1}{24} \right) \\= \frac{ LCM\: of \: numerators }{HCF \: of \: denominators } \\= \frac{ LCM (1,1) )}{HCF (18,24)}\\= \frac{1}{6}$

$i ) HCF \:of \: \left( \frac{1}{18}, \frac{1}{24} \right) \\= \frac{ HCF\: of \: numerators }{LCM \: of \: denominators } \\= \frac{ HCF(1,1) )}{LCM (18,24)}\\= \frac{1}{72}$

Therefore.,

$\red{LCM \: of \: reciprocals \: of \: 18 \:and \:24 }$

$\green {= \frac{1}{6}}$

$\red{HCF \: of \: reciprocals \: of \: 18 \:and \:24 }$

$\green {= \frac{1}{72}}$

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