Question

find the lcm and hcf of 180,144 and 192 by applying prime factorization method

Answer 1

Answer:

prime factorization of 180 =2×2×3×3×5

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {2}^{2} \times {3}^{2} \times {5}^{1}$

prime factorization of 144 = 2×2×2×2×3

×3

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {2}^{4} \times {3}^{2}$

prime factorization of 192 = 2×2×2×2×2

×2×3

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {2}^{6} \times {3}^{1}$

LCM of 180, 144 and 192= 2×2×2×2×2×2

×3×3×5

=2880

HCF of 180, 144 and 192 = 2×2×3

=12