Question

find the hcf and lcm of 180,144 and 90 by prime factorisation

Answer 1

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Answer 2

Answer:

The HCF(180,144,90)=18

The LCM(180,144,90)=720

Step-by-step explanation:

Given : Numbers 180,144 and 90

To find : The HCF and LCM of the given numbers by prime factorization.

Solution :

Prime factorization of the numbers 180, 144,90

$180=2\times2\times3\times3\times5$

$144=2\times2\times2\times2\times3\times3$

$90=2\times3\times3\times5$

HCF is the highest common factor.

$HCF(180,144,90)=2\times3\times3=18$

The HCF(180,144,90)=18

The LCM is the least common factor

2     |     180   144    90

2     |     90      72     45

2     |     45     36     45

2     |     45     18      45

3     |     45      9       45

3     |      15      3        45

5     |      5        1         5

             1         1          1

The LCM= $2\times2\times2\times2\times3\times3\times5=720$

The LCM(180,144,90)=720