Here is the solution for Telangana Class 10th SCERT Mathematics, Chapter number 1, Exercise 1.2 question number 2 which is Find the LCM and HCF of the following integers by the prime factorization method.
Telangana SCERT Class 10, Exercise 1.2 Question number 2 with all bits.
2) Find the LCM and HCF of the following integers by the prime factorization method.
i) 12, 15 and 21.
Solution: Given,
Prime Factorization:-
12 = 2 x 2 x 3.
15 = 3 x 5.
21 = 3 x 7.
The common number which occurs once in all the factors is 3.
(Therefore: HCF = 3).
ii) 17, 23 and 29.
Solution: Given,
Prime Factorization:-
17 = 1.
23 = 1.
29 = 1.
The common number which occurs once in all the factors is 1.
(Therefore: HCF = 1).
(Therefore: LCM = 17 x 23 x 29 = 11339).
iv) 72 and 108.
Solution: Given,
Prime Factorization:-
72 = 2 x 2 x 2 x 3 x 3 x 1
108 = 2 x 2 x 3 x 3 x 3 x 1
HCF = 36
LCM = 2 x 2 x 2 x 3 x 3 x 3 = 216
