Chapter CSB1.3, Problem 20E

To determine

To find: the LCM of monomials $75n^2,25n^4$ .

Answer to Problem 20E

The LCM of numbers is $75n^4$ .

Explanation of Solution

Given:

The monomials are $75n^2$ and $25n^4$ .

Calculation:

LCM means least common multiple. Least common multiple of two numbers or monomials (say a and b ) is the smallest positive number or monomial which is divisible by either the numbers or monomials ( b and a ).

Factorize each monomial as follows:

  $\begin{array}{c}75n^2=5\times 5\times 3\times n\times n\\ 25n^4=5\times 5\times n\times n\times n\times n\end{array}$

LCM of the numbers is,

  $\text{LCM}=5\times 5\times 3\times n\times n\times n\times n=75n^4$

Thus, the LCM of numbers is $75n^4$ .