Question

find the LCM of 225,27,171 by prime fatorization method​

Answer 1

Question:

• Find the LCM of 225,27,171 by prime fatorization method

Solution:

• To find LCM of 225,27 and 171 , write each number as a product of prime factors

$\sf{225 = \: 3 \times 3 \times 5 \times 5} = {3}^{2} \times {5}^{2}$

$27 = 3 \times 3 \times 3 = {3}^{3}$

$171 = 3 \times 3 \times 19 = {3}^{2} \times {19}^{1}$

• LCM of 225 , 27 and 171

$\sf{ = 3 \times 3 \times 3 \times 5 \times 5 \times 19 }$

$\sf \textbf{ = 12825}$

• In exponential form LCM

$\sf{ = {3}^{3} \times {5}^{2} \times {19}^{1} = 12825 }$

$\sf \therefore \: {Required \: LCM \: is \: 12825}$