Question

Find the HCF and LCM of 144, 180 and 192 by prime factorisation method.
(A) 12, 2880
(B) 4. 2880
(C) 12. 1440
(D) 4, 1440​

Answer 1

Answer:

2880

Step-by-step explanation:

N/A

Answer 2

Step-by-step explanation:

Solution

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Using the factor tree for the prime factorization of 144,180 and 192, we have

144=2

4

×3

2

,180=2

2

×3

2

×5 and 192=2

6

×3

To find the HCF, we list the common prime factor and their smallest exponents in 144,180 and 192 as follows:

Common prime factor Least exponents

2 2

3 1

∴ HCF=2

2

×3

1

=12

To find the LCM, we list all prime factors of 144,180,192 and their greatest exponents as follows:

Prime factors of 144,180 and 192 Greatest exponents

2 6

3 2

5 1

∴ LCM=2

6

×3

2

×5

1

=64×9×5=2880