Question

if the HCF of 65 and 117 is expressible in the following 65m-117, then the value of m is ....
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Answer 1

ur answer is 2

Step-by-step explanation:

By Euclid’s division algorithm

b=aq+r

117=65×1+52

65=52×1+13

52=13×4+0

H.C.F(65,117)=13

Since H.C.F =65m-117

so, 65m-117=13

=65m=13+117=130

=m=130/65=2

Answer 2

QUESTION -

if the HCF of 65 and 117 is expressible in the following 65m-117, then the value of m is ....

if the HCF of 65 and 117 is expressible in the following 65m-117, then the value of m is ....

ANSWER -

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

@HarshPratapSingh