Find the Least Common Multiple (LCM) of $62$, $53$ and $44$.

To find the LCM, let's find the prime factors of each number:
$62=2\times 31$
$53=53$ (Prime number)
$44=2^2\times 11$

LCM is the product of the highest power of each prime factor involved:

$$\text{LCM}=2^2\times 11\times 31\times 53$$

$$\text{LCM}=4\times 11\times 31\times 53$$

$$\text{LCM}=44\times 31\times 53$$

$$44\times 31=1364$$

$$1364\times 53=72292$$

Wait, looking at the provided options, there seems to be a discrepancy in the problem text ($62^{62}$ format vs standard LCM). Based on standard LCM calculation for $\{62,53,44\}$, the value is $72292$. However, if we evaluate the original options provided in the source material:
Option C is $134900$ (No match for simple LCM).
Let's re-examine $44\times 62\times 53/\text{HCF}$.
$\text{HCF}(62,44)=2$.
$\text{LCM}(62,44)=\frac{62\times 44}{2}=1364$.
$\text{LCM}(1364,53)=1364\times 53=72292$.
Note: Due to potential typo in source values, if the answer is intended as C based on the provided list, it reflects a source error. Calculation follows standard LCM logic.