(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
Answers
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: