Question

1. Find the greatest common divisor of the term 144x3y2and 81xy4​

Answer 1

`1296x^3y^4`

Explanation:

Given the terms:

`144x^3y^2`

and
`81xy^4`

To find:

Greatest Common Divisor of the two terms or Least Common Multiple (LCM) of two numbers = ?

Solution:

First of all, let us find the HCF (Highest Common Factor) for both the terms.

i.e. the terms which are common to both.

Let us factorize them.

`144x^3y^2 = \underline{3 * 3} * 16* \underline x * x^(2)* \underline{y^(2) }`

`81xy^4= \underline {3* 3}* 9 * \underline{x} * \underline{y^2}* y^2`

Common terms are underlined.

So, HCF of the terms =
`9xy^2`

Now, we know the property that product of two numbers is equal to the product of the numbers themselves.

HCF
`*` LCM =
`144x^3y^2`
`*`
`81xy^4`

`LCM = (144x^3y^2 * 81xy^4)/(9xy^2)\\\Rightarrow LCM = 144x^3y^2 * 9x^(1-1)y^(4-2)\\\Rightarrow LCM = 144x^3y^2 * 9x^(0)y^(2)\\\Rightarrow LCM = \bold{1296x^3y^4 }`