Question

The LCM of $4^5$, $4^{-81}$, $4^{12}$, and $4^7$ is

• A. $4^{-81}$
• B. $4^5$
• C. $4^{12}$
• D. $4^7$

Answer 1

The correct option is C $4^{12}$

We write the given numbers in fractions as follows:

$4^5=\frac{4^5}{1}$

$4^{-81}=\frac{1}{4^{81}}$

$4^{12}=\frac{4^{12}}{1}$

$4^7=\frac{4^7}{1}$

We know that LCM of two or more fractions is given by LCM of Numerators divided by HCF of Denominators and thus

LCM of the numerators $(4^5,1,4^{12},4^7)=4^{12}$

HCF of the denominators $(1,4^{81},1,1)=1$

Therefore,

LCM$(4^5,4^{-81},4^{12},4^7)=\frac{4^{12}}{10}=4^{12}$

Hence, the LCM is $4^{12}$.