Question

Find HCF and LCM of 144 and 76

Answer 1

Given:

Numbers 144 and 76

Find :

HCF and LCM of 144 and 76 = ?

Solution:

(1) Find HCF of 144 and 76

=>  For find the HCF, first find the prime factorization of both numbers.

• So for 144:

        144 = 2 × 2 × 2 × 2 × 3 × 3

• For 76:

        76 = 2 × 2 × 19

=>  To find the HCF, we have to multiply all the prime factors common to both numbers:

=>  In both number common factors are 2 × 2

HCF = 2 × 2

HCF = 4

(2) Find LCM of 144 and 76

=>  For find the LCM, first find the prime factorization of both numbers.

• So for 144:

        144 = 2 × 2 × 2 × 2 × 3 × 3

• For 76:

        76 = 2 × 2 × 19

=>  To find the, multiply each factor the greater number of times it occurs

LCM =  2 × 2 × 2 × 2 × 3 × 3 × 19

LCM = 2736

Hence the HCF of 144 and 76 is 4, And LCM of 144 and 76 is 2736