Using prime factorisation, find the HCF and LCM of :
(i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29
(iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36, 45
Using prime factorisation, find the HCF and LCM of :
(i) 8, 9, 25 (ii) 12, 15, 21 (iii) 17, 23, 29
(iv) 24, 36, 40 (v) 30, 72, 432 (vi) 21, 28, 36, 45
Sol:
(i) 8 = 2 x 2 x 2 = 23
9 = 3 x 3 = 32
25 = 5 x 5 = 52
HCF = Product of smallest power of each common prime factor in the numbers = 1
LCM = Product of the greatest power of each prime factor involved in the numbers = 23 x 32x 52 = 1800
(ii) 12 = 2 x 2 x 3 = 22 x 3
15 = 3 x 5
21 = 3 x 7
HCF = Product of smallest power of each common prime factor in the numbers = 3
LCM = Product of the greatest power of each prime factor involved in the numbers = 22 x 3 x 5 x 7 = 420
(iii) 17 = 17
23 = 23
29 = 29
HCF = Product of smallest power of each common prime factor in the numbers = 1
LCM = Product of the greatest power of each prime factor involved in the numbers = 17 x 23 x 29 = 11339
(iv) 24 = 2 x 2 x 2 x 3 = 23 x 3
36 = 2 x 2 x 3 x 3 = 22 x 32
40= 2 x 2 x 2 x 5 = 23 x 5
Therefore, HCF = Product of smallest power of each common prime factor in the numbers = 22 = 4
Therefore, LCM = Product of the greatest power of each prime factor involved in the numbers = 23 x 32 x 5 = 360
(v) 30 = 2 x 3 x 5
72=2x2x2x3x3=23x32
432.2x2x2x2x3x3x3=24 x 33
Therefore, HCF = Product of smallest power of each common prime factor in the numbers = 2 x 3 = 6
Therefore, LCM = Product of the greatest power of each prime factor involved in the numbers = 24 x 33 x 5 = 2160
(vi) 21 = 3 x 7
28 = 28 = 2 x 2 x 7 = 22 x 7
36 = 2 x 2 x 3 x 3 = 22 x 32
45 = 5 x 3 x 3 = 5 x 32
Therefore, HCF = Product of smallest power of each common prime factor in the numbers = 1
Therefore, LCM = Product of the greatest power of each prime factor involved in the numbers = 22 x 32 x 5 x 7 = 1260
Sol:
(i) 8 = 2 x 2 x 2 = 23
9 = 3 x 3 = 32
25 = 5 x 5 = 52
HCF = Product of smallest power of each common prime factor in the numbers = 1
LCM = Product of the greatest power of each prime factor involved in the numbers = 23 x 32x 52 = 1800
(ii) 12 = 2 x 2 x 3 = 22 x 3
15 = 3 x 5
21 = 3 x 7
HCF = Product of smallest power of each common prime factor in the numbers = 3
LCM = Product of the greatest power of each prime factor involved in the numbers = 22 x 3 x 5 x 7 = 420
(iii) 17 = 17
23 = 23
29 = 29
HCF = Product of smallest power of each common prime factor in the numbers = 1
LCM = Product of the greatest power of each prime factor involved in the numbers = 17 x 23 x 29 = 11339
(iv) 24 = 2 x 2 x 2 x 3 = 23 x 3
36 = 2 x 2 x 3 x 3 = 22 x 32
40= 2 x 2 x 2 x 5 = 23 x 5
Therefore, HCF = Product of smallest power of each common prime factor in the numbers = 22 = 4
Therefore, LCM = Product of the greatest power of each prime factor involved in the numbers = 23 x 32 x 5 = 360
(v) 30 = 2 x 3 x 5
72=2x2x2x3x3=23x32
432.2x2x2x2x3x3x3=24 x 33
Therefore, HCF = Product of smallest power of each common prime factor in the numbers = 2 x 3 = 6
Therefore, LCM = Product of the greatest power of each prime factor involved in the numbers = 24 x 33 x 5 = 2160
(vi) 21 = 3 x 7
28 = 28 = 2 x 2 x 7 = 22 x 7
36 = 2 x 2 x 3 x 3 = 22 x 32
45 = 5 x 3 x 3 = 5 x 32
Therefore, HCF = Product of smallest power of each common prime factor in the numbers = 1
Therefore, LCM = Product of the greatest power of each prime factor involved in the numbers = 22 x 32 x 5 x 7 = 1260
