Question

Find the HCF and LCM. 

i. 14,28 

ii. 32,16 

iii. 17,102,170 

iv. 23,69

v. 21,49,84

Answer 1

i. 14 = 2 x 7 

28 = 2 x 14 

= 2 x 2 x 7 

∴ HCF of 14 and 28 = 2 x 7 

= 14 

LCM of 14 and 

28 = 2 x 2 x 7 

= 28 

ii. 32 = 2 x 16 

= 2 x 2 x 8 

= 2 x 2 x 2 x 4 

= 2 x 2 x 2 x 2 x 2

16 = 2 x 8 

= 2 x 2 x 4 

= 2 x 2 x 2 x 2 

∴ HCF of 32 and 16 = 2 x 2 x 2 x 2 

= 16

∴ LCM of 32 and 16 = 2 x 2 x 2 x 2 x 2 = 32 

iii. 17 = 17 x 1 

102 = 2 x 51 

= 2 x 3 x 17 

170 = 2 x 85 

= 2 x 5 x 17 

∴ HCF of 17, 102 and 170 = 17 

∴ LCM of 17, 102 and 170 = 17 x 2 x 3 x 5 

= 510

iv. 23 = 23 x 1 

69 = 3 x 23 

∴ HCF of 23 and 69 = 23 

∴ LCM of 23 and 69 = 23 x 3 = 69 

v. 21 = 3 x 7 

49 = 7 x 7 

84 = 2 x 42 

= 2 x 2 x 21 

= 2 x 2 x 3 x 7 

∴ HCF of 21, 49 and 84 = 7 

∴ LCM of 21, 49 and 84 = 7 x 3 x 7 x 2 x 2 

= 588