Question

Find the greatest number that will divide 65 and 117 is expressible on the form 65m-117. Find the value of m also find the lcm of 65 and 117 using prime factorisation

Answer 1

Solution :-

H.C.F. of 65 and 117 by Euclid's Division Lemma.

⇒ 117 = (1*65) + 52

⇒ 65 = (1*52) + 13

⇒ 52 = (4*13) + 0

Therefore, H.C.F. of 65 and 117 is 13.

65m - 117 = 13

⇒ 65m = 13 + 117

⇒ 65m = 130

⇒ m = 130/65

⇒ m = 2

Now, L.C.M. of 65 and 117

65 = 5*13

117 = 3*3*13

L.C.M. of 65 and 117 = 3*3*5*13

L.C.M. of 65 and 117 = 585

Answer.

Answer 2

The correct answer is= 13