**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 = 3^{2} x 13

=> LCM(65, 117) = 3^{2} x 5 x 13 = 585