# 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

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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

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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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