Q. 1.6 - Intermediate Algebra

Question

Find the LCM of 18 and 24 using the Prime Factors method.

Step-by-Step Solution

Answer

The LCM of 18 and 24 is 72.

Step 1 . Given Information.

The given numbers, to find the LCM, is 18 and 24.

Step 2. Find the prime factors.

Find the prime factors of the given numbers.

$18=2\times 3\times 3$

And,

$24=2\times 2\times 2\times 3$

Now, make the list of primes factors from each number.

$$\begin{gathered} 18=2\times 3\times 3 \\ 24=2\times 2\times 2\times 3 \end{gathered}$$

Step 3. Check common and single factors.

$\text{LCM=72}$Take out the common factors and single factors.

$$\begin{gathered} \underline{24=2\times 2\times 2\times 3 \\ 18=2 \times 3\times 3} \\ LCM=2\times 2\times 2\times 3\times 3 \end{gathered}$$

Multiply the factors for LCM.

Step 4. Conclusion.

The required LCM is 72.