Question

for the pair of numbers 480 and 512 verify that the product of two numbers is equal to the product of hcf and lcm

Answer 1

Step-by-step explanation:

$480 = 2 \times 3 \times 2 \times 2 \times 2 \times 2 \times 5 = {2}^{5} \times 3 \times 5$

$512 = {8}^{3} = {(2 \times 2 \times 2)}^{3} = {2}^{9}$

$hcf = {2}^{5} \times {3}^{0} \times {5}^{0} = {2}^{5} \times 1 \times 1 = 32$

$lcm = {2}^{9} \times 3 \times 5 = 7680$

$we \: need \: to \: verify \: \: \: lcm \times hcf = product \: of \: two \: numbers$

$solving \: lhs$

$32 \times 7680 = 245760$

$solving \: rhs$

$480 \times 512 = 245760 = lhs$

$hence \: verified$