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

let us find the HCF of 65 and 117,

117 = 1×65 + 52

65 = 1× 52 + 13

52 = 4 ×13 +0

therefore HCF of 65 and 117 is 13.

65m-117 = 13

65m = 117+13 = 130

m =130/65 =2

Now, 65 = 5 × 13

117 = 13 × 3 × 3

LCM of 65 and 117 = 5 × 13 × 3 × 3 = 585