Question

the HCF of 65 and 117 is of the expression in the form 65m-117 find the value of m also find the lcm of 65 and 117 using prime factorisation method.

Answer 1

117 = 1×65 + 52

65 = 1× 52 + 13

52 = 4 ×13 + 0

∴ 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.