Question

if a, b , c are three positive integers and b is the only common factor of a and c, then lcm (a, b, c) then hcf of a,b,c is​

Answer 1

Answer:

LCM(a, b, c) = bk, where k = k₁k₂

HCF(a, b, c) = b

Step-by-step explanation:

Given that a, b, c are three positive integers and b is the only common factor of a and c.

Let a = bk₁ and c = bk₂ where k₁ and k₂ are unequal factors of a and c

Then LCM(a, b, c)

= LCM(bk₁, b, bk₂)

= bk₁k₂

= bk, where k₁k₂ = k

and HCF(a, b, c)

= HCF(bk₁, b, bk₂)

= b

Answer 2

Answer:

lcm (a, b, c) = ac/b

hcf of a,b,c is​ b

Step-by-step explanation:

if a, b , c are three positive integers and b is the only common factor of a and c

=> a  = bx

&   c = by

& x & y are co prime

a = b * x

b = b * 1

c = b * y

x & y co prime (no common factor)

HCF = b

LCM = b * x  * y

= b * x * b * y / b

= a * c / b

= ac/b

lcm (a, b, c) = ac/b

hcf of a,b,c is​ b