Question

(a) 10, 15 (b) 35, 40 (c) 32, 48 2. Find HCF and LCM by using the property in Question no. 1. (a) 27, 90 (b) 145, 232 (c) 117, 221​

Answer 1

Answer:

1.

The HCF of 27 and 90 is 9.

Steps to find GCF

Find the prime factorization of 27

27 = 3 × 3 × 3

Find the prime factorization of 90

90 = 2 × 3 × 3 × 5

To find the HCF, multiply all the prime factors common to both numbers:

Therefore, HCF = 3 × 3

GCF = 9

The lcm of 27 and 90 is 270.

Steps to find LCM

Find the prime factorization of 27

27 = 3 × 3 × 3

Find the prime factorization of 90

90 = 2 × 3 × 3 × 5

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 3 × 3 × 3 × 5

LCM = 270

2.

The gcf of 145 and 232 is 29.

Steps to find GCF

Find the prime factorization of 145

145 = 5 × 29

Find the prime factorization of 232

232 = 2 × 2 × 2 × 29

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 29

he lcm of 145 and 232 is 1160.

Steps to find LCM

Find the prime factorization of 145

145 = 5 × 29

Find the prime factorization of 232

232 = 2 × 2 × 2 × 29

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 2 × 2 × 2 × 5 × 29

LCM = 1160

3.

The gcf of 117 and 221 is 13.

Steps to find GCF

Find the prime factorization of 117

117 = 3 × 3 × 13

Find the prime factorization of 221

221 = 13 × 17

To find the gcf, multiply all the prime factors common to both numbers:

Therefore, GCF = 13

Find the prime factorization of 117

117 = 3 × 3 × 13

Find the prime factorization of 221

221 = 13 × 17

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 3 × 3 × 13 × 17

LCM = 1989

explanation: