Question

Find the HCF of 105 and 1515by prime factorisation method and hence find its LCM

Answer 1

Hi ,

Expressing 105 and 1515 as product

of primes

105 = 3 × 5 × 7

1515 = 3 × 5 × 101

HCF ( 105, 1515 ) = 3 × 5 = 15

We know that ,
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For any two positive integers a and b

HCF( a , b ) × LCM( a , b ) = a × b

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Here ,

a = 105 , b = 1515

HCF( 105 , 1515 ) = 15 ,

LCM = ?

HCF × LCM = 105 × 1515

15 × LCM = 105 × 1515

LCM = ( 105 × 1515 ) / 15

= 105 × 101

LCM ( 105 , 1515 )= 10605

I hope this helps you.

:)

Answer 2

Hi

Here is your answer !

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solution
______

3 | 105
______
5 | 35
____
7

and ,

3 | 1515
______
5 | 505
_____
101

Now ,

Prime factorisation

105 = 3 × 5 × 7

1515 = 3 × 5 × 101

.°. HCF = 3 × 5 = 15

and

LCM = 3 × 5 × 7 × 101 = 10605

thanks

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