Question

If the lcm and hcf of two numbers are equal and the product of two numbers is 729 find their lcm

Answer 1

Hey,sup!

As per the question,

LCM and HCF are equal.

So, Product of two numbers= LCM×HCF.

=> 729= LCM×LCM. (LCM=HCF)

=>LCM^2=729.

=>LCM=√729= 27.

The their LCM is 27.

Hope it helps.

Answer 2

Given:

The product of the two numbers is 729.

To find:

The LCM.

Solution:

The LCM of the two numbers is 27.

To answer this question, we will follow the following steps:

First of all, we should know that the product of two numbers a and b is equal to the multiplication of their HCF and LCM.

This means,

$a \times b = HCF \times LCM$

Now,

as given in the question,

The product of two numbers = 729

Let the LCM of two numbers be x.

So,

HCF of two numbers will also be x. (as given)

Thus,

$729 = x \times x$

$729 = {x}^{2}$

After taking square root on both sides,

We get,

$x = 27$

(as x cannot be -27, so x = -27 is neglected)

Hence, the LCM of the two numbers is 27.