Chapter 7.7, Problem 34E

To determine

To find: the least common multiple of $40,50$

Answer to Problem 34E

The Least common multiple of $40,50$ is $200$

Explanation of Solution

Given information: Consider, the number $40,50$ provided in the question

Calculation:

To evaluate the least common multiple of $40,50$ , it is needed to list the common factors of each number

Therefore,

  $\begin{array}{l}\text{factor}\text{of}40=2\cdot 2\cdot 2\cdot 5\\ \text{factor}\text{of}50=2\cdot 5\cdot 5\end{array}$

Now multiply all the factors, using each common factor only once

  $\begin{array}{l}\text{Least common multiple of}40,50=2\cdot 2\cdot 2\cdot 5\cdot 5\\ \Rightarrow \text{Least common multiple of 40},50=200\end{array}$

Hence,

The Least common multiple of $40,50$ is $200$