Question

Find the prime factors of the following numbers and find their LCM and HCF.
(i) 75, 135 (ii) 114, 76 (iii) 153, 187 (iv) 32, 24, 48​

Answer 1

Answer:

i. 75 = 3 × 25  = 3 × 5 × 5

135 = 3 × 45  = 3 × 3 × 15  = 3 × 3 × 3 × 5

∴ HCF of 75 and 135 = 3 × 5  = 15

LCM of 75 and 135 = 3 × 5 × 5 × 3 × 3  = 675

ii. 114 = 2 × 57  = 2 × 3 × 19  76 = 2 × 38  = 2 × 2 × 19

 ∴ HCF of 114 and 76 = 2 × 19 = 38

LCM of 114 and 76 = 2 × 19 × 3 × 2  = 228

iii. 153 = 3 × 51  = 3 × 3 × 17  187 = 11 × 17

∴ HCF of 153 and 187 = 17  LCM of 153 and 187 = 17 × 3 × 3 × 11  = 1683

v. 32 = 2 × 16  = 2 × 2 × 8  = 2 × 2 × 2 × 4  = 2 × 2 × 2 × 2 × 2  24 = 2 × 12  = 2 × 2 × 6  = 2 × 2 × 2 × 3  48 = 2 × 24  = 2 × 2 × 12  = 2 × 2 × 2 × 6  = 2 × 2 × 2 × 2 × 3

∴ HCF of 32, 24 and 48 = 2 × 2 × 2  = 8  LCM of 32,24 and 48 = 2 × 2 × 2 × 2 × 2 × 3  = 96

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