Find HCF and LCM by using the property in Question no. 1.
(a) 27, 90
(b) 145, 232
(c) 117, 221
Answers
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
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Answer:
HCF OF ( 27 , 90 ) IS 6
LCM OF ( 27 , 90 ) IS 270
HCF OF ( 145 , 132 ) IS 29
LCM OF ( 145 , 232 ) IS 1160
HCF OF ( 117 , 221 ) IS 13
LCM OF ( 117 , 221 ) IS 1989