Divide the numbers by the smallest prime number that divides at least one of them.

Question

ScanSolve AI Tutor · Accepted Answer

To find the Least Common Multiple (LCM) of 4, 20, and 18 using the division method:

Divide the numbers by the smallest prime number that divides at least one of them.
$\begin{array}{c|ccc} 2 & 4, & 20, & 18 \\ \hline & 2, & 10, & 9 \end{array}$
Continue dividing the resulting numbers by the smallest prime number.
$\begin{array}{c|ccc} 2 & 4, & 20, & 18 \\ \hline 2 & 2, & 10, & 9 \\ \hline & 1, & 5, & 9 \end{array}$
Continue dividing.
Since 9 is divisible by 3, use 3.
$\begin{array}{c|ccc} 2 & 4, & 20, & 18 \\ \hline 2 & 2, & 10, & 9 \\ \hline 3 & 1, & 5, & 9 \\ \hline & 1, & 5, & 3 \end{array}$
Continue dividing by 3.
$\begin{array}{c|ccc} 2 & 4, & 20, & 18 \\ \hline 2 & 2, & 10, & 9 \\ \hline 3 & 1, & 5, & 9 \\ \hline 3 & 1, & 5, & 3 \\ \hline & 1, & 5, & 1 \end{array}$
Continue dividing by 5 until all numbers are 1.
$\begin{array}{c|ccc} 2 & 4, & 20, & 18 \\ \hline 2 & 2, & 10, & 9 \\ \hline 3 & 1, & 5, & 9 \\ \hline 3 & 1, & 5, & 3 \\ \hline 5 & 1, & 5, & 1 \\ \hline & 1, & 1, & 1 \end{array}$
Multiply all the prime divisors to find the LCM.
$\text{LCM} = 2 \times 2 \times 3 \times 3 \times 5 = 4 \times 9 \times 5 = 36 \times 5 = 180$
The LCM of 4, 20, and 18 is $\boxed{\text{180}}$ .

Answer