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)/HCF (a,b,c)​

Answer 1

Answer:

HCF = b

LCM = ac/b

LCM/HCF = (ac/b)/b = ac/b²

I hope it's correct....

Answer 2

$\frac{LCM}{HCF}=\frac{ac}{b^2}$

Step-by-step explanation:

Consider the provided information.

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

The common factor of a and b is c.

So we can say that a = bx

and c=by

Where x and y are co-prime

Thus the three positive integers a, b and c can be written as:

a = bx

b = b×1

c = by

Thus, the HCF of a, b and c = b  (Because b is the only common factor among them.)

The LCM of a, b and c = $b\times x\times y$

The LCM of a, b and c = $b\times x\times y\times\frac{b}{b}$

The LCM of a, b and c = $\frac{b\times x\times y\times b}{b}=\frac{ac}{b}$

We need to find LCM (a,b,c)/HCF (a,b,c)​

So divide LCM with HCF

$\frac{LCM}{HCF}=\frac{\frac{ac}{b}}{b}$

$\frac{LCM}{HCF}=\frac{ac}{b^2}$

Hence, $\frac{LCM}{HCF}=\frac{ac}{b^2}$

#Learn more

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​

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