Question

The HCF of 65 and 117 is expressible in the form 65m – 117. Find the value of m. also find
the LCM of 65 and 117 using prime factorization method.​

Answer 1

Answer:

firstly , we find the HCF of 65 and 117

117 = 65*1+52

65=52*1+13

52=13*4+0

so, hcf of 65 and 117 is 13

but. hcf of 65 and 117 express in  a form of 65m-117

therefore, 65m-117=13

=> 65m = 117+13=130

=> m = 130/65

=> m = 2

now, prime factorisation of 65 and 117 is --

65 = 5*13 and 117 = 3*3*13

so, its LCM is 

13*5*3*3=585

hope it help you