Using prime factorization, find the HCF and LCM of:
$30, 72, 432$

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Solution

$30 = 2 \times 3 \times 5 = 2^{1} \times 3^{1} \times 5^{1}$
$72 = 2^{3} \times 3^{2} = 2^{3} \times 3^{2} \times 5^{0}$
$432 = 2^{4} \times 3^{3} = 2^{4} \times 3^{3} \times 5^{0}$
From the above
$H C F = 2^{1} \times 3^{1} \times 5^{0} = 6$
$L C M = 2^{4} \times 3^{3} \times 5^{1} = 2160$

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