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

Solution:
117 = 65 x 1 + 52
65 = 52 x 1 + 13
65 = 13 x 5 + 0
=> HCF(65, 117) = 13
Since, HCF(65, 117) = 65m - 117
=> 13 = 65m - 117
=> 65m = 117 + 13 = 130
=> m = 130/65 = 2
Now, 65 = 5 x 13
and 117 = 3 x 3 x 13 = 3² x 13
=> LCM(65, 117) = 3² x 5 x 13 = 585