Question

Find the LCM and HCF of 72,108.

Answer 1

$We \:have , \\72 = 2\times 2 \times 2 \times 3 \times 3 = 2^{3} \times 3^{2}$

$108 = 2\times 2 \times 3 \times 3\times 3 = 2^{2} \times 3^{3}$

$HCF (72,108) = 2^{2} \times 3^{2} \\= 4 \times 9 \\= 36$

$\pink {( Product \:of \:the \: smallest \:power }\\\pink { of \:each \: common \:prime \: factors \:of }\\\pink { the \: numbers )}$

$LCM (72,108) = 2^{3} \times 3^{3} \\= 8 \times 27 \\= 216$

$\blue {( Product \:of \: the \: greatest \: power} \\\blue { of \: each \:prime \: factors \:of \:the \: numbers)}$

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