Question

find the HCF and LCM of foll. using FUNDAMENTAL THEOREM of ARITHMETIC method (Prime Factorization)

1)96 and 404

2)6,72 and 120

3)26 and 91

4)6 and 20

5)17,23 and 29

6)8,9 and 25

7)426 and 576

8)26676 and 337554

9)1376 and 15428

10)11008 and 7344

11)625,1125 and 2125

12)448,1008 and168

13)270,405 and 315

14)377,435 and 667

Answer 1

Ans-
Hope this helps you ;)

Answer 2

Given:

1)96 and 404 , 2)6,72 and 120, 3)26 and 91 , 4)6 and 20 , 5)17,23 and 29 , 6)8,9 and 25 , 7)426 and 576 , 8)26676 and 337554, 9)1376 and 15428 ,  10)11008 and 7344 , 11)625,1125 and 2125 , 12)448,1008 and168  13)270,405 and 315 , 14)377,435 and 667

To find:

The H.C.F and L.C.M of the following by using prime factorization method

Solution:

(1). 96 and 404

96 = 2 × 2 × 2 × 2 × 2 × 3

404 = 2 × 2 × 101

∴ H.C.F. = 2 × 2 = 4

∴ L.C.M. = 2 × 2 × 2 × 2 × 2 × 3 × 101 = 9696

(2). 6, 72 and 120

6 = 2 × 3

72 = 2 × 2 × 2 × 3 × 3

120 = 2 × 2 × 2 × 3 × 5

∴ H.C.F. = 2 × 3 = 6

∴ L.C.M. = 2 × 2 × 2 × 3 × 3 × 5 = 360

(3). 26 and 91

26 = 2 × 13

91 = 7 × 13

∴ H.C.F. = 13

∴ L.C.M. = 2 × 7 × 13 = 182

(4). 6 and 20

6 = 2 × 3

20 = 2 × 2 × 5

∴ H.C.F. = 2

∴ L.C.M. = 2 × 2 × 3 × 5 = 60

(5). 17, 23 and 29

17 = 1 × 17

23 = 1 × 23

29 = 1 × 29

∴ H.C.F. = 1

∴ L.C.M. = 17 × 23 × 29 = 11339

(6). 8, 9 and 25

8 = 2 × 2 × 2

9 = 3 × 3

25 = 5 × 5

∴ H.C.F. = 1

∴ L.C.M. = 2 × 2 × 2 × 3 × 3 × 5 × 5 = 1800

(7). 426 and 576

426 = 2 × 3 × 71

576 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

∴ H.C.F. = 2 × 3 = 6

∴ L.C.M. = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 71 = 40896

(8). 26676 and 337554

26676 = 2 × 2 × 3 × 3 × 3 × 13 × 19

337554 = 2 × 3 × 3 × 3 × 7 × 19 × 47

∴ H.C.F. = 2 × 3 × 3 × 3 × 19 = 1026

∴ L.C.M. = 2 × 2 × 3 × 3 × 3 × 7 × 13 × 19 × 47 = 8776404

(9). 1376 and 15428

1376 = 2 × 2 × 2 × 2 × 2 × 43

15428 = 2 x 2 x 7 x 19 x 29

∴ H.C.F. = 2 × 2 = 4

∴ L.C.M. = 2 × 2 × 2 × 2 × 2 × 7 × 19 × 29 × 43 = 5307232

(10). 11008 and 7344

1376 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 17

15428 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 43

∴ H.C.F. = 2 × 2 × 2 × 2 = 16

∴ L.C.M. = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 17 × 43 = 5052672

(11). 625, 1125 and 2125

625 = 5 × 5 × 5 × 5

1125 = 3 × 3 × 5 × 5 × 5

2125 = 5 × 5 × 5 × 17

∴ H.C.F. = 5 × 5 × 5 = 125

∴ L.C.M. = 3 × 3 × 5 × 5 × 5 × 5 × 17 = 95625

(12). 448, 1008 and 168

448 = 2 × 2 × 2 × 2 × 2 × 2 × 7

1008 = 2 × 2 × 2 × 2 × 3 × 3 × 7

168 = 2 × 2 × 2 × 3 × 7

∴ H.C.F. = 2 × 2 × 2 × 7 = 56

∴ L.C.M. =  2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 = 4032

(13). 270, 405 and 315

270 = 2 × 3 × 3 × 3 × 5

405 = 3 × 3 × 3 × 3 × 5

315 = 3 × 3 × 5 × 7

∴ H.C.F. = 3 × 3 × 3 × 5 = 45

∴ L.C.M. =  2 × 3 × 3 × 3 × 3 × 5 × 7 = 5670

(14). 377, 435 and 667

377 = 13 × 29

435 = 3 × 5 × 29

667 = 23 × 29

∴ H.C.F. = 29

∴ L.C.M. =  3 × 5 × 13 × 23 × 29 = 130065

------------------------------------------------------------------------------------

Also View:

Find the HCF and LCM of 306 and 657by prime factorization method

https://brainly.in/question/1241341

Find hcf and lcm of 90 and 144 by the prime factorization method

https://brainly.in/question/1244287