Find the LCM of 150 and 300 using the common division method.

Question

ScanSolve AI Tutor · Accepted Answer

To find the LCM of 150 and 300 using the common division method, we divide the numbers by common prime factors until no two numbers have a common prime factor.

Divide 150 and 300 by a common prime factor, starting with 2.
$\begin{array}{c|cc} 2 & 150 & 300 \\ \hline & 75 & 150 \end{array}$
Divide 75 and 150 by a common prime factor, which is 3.
$\begin{array}{c|cc} 2 & 150 & 300 \\ 3 & 75 & 150 \\ \hline & 25 & 50 \end{array}$
Divide 25 and 50 by a common prime factor, which is 5.
$\begin{array}{c|cc} 2 & 150 & 300 \\ 3 & 75 & 150 \\ 5 & 25 & 50 \\ \hline & 5 & 10 \end{array}$
Divide 5 and 10 by a common prime factor, which is 5.
$\begin{array}{c|cc} 2 & 150 & 300 \\ 3 & 75 & 150 \\ 5 & 25 & 50 \\ 5 & 5 & 10 \\ \hline & 1 & 2 \end{array}$
The remaining numbers, 1 and 2, have no common prime factors other than 1.
To find the LCM, multiply all the divisors and the remaining numbers.
$\text{LCM} = 2 \times 3 \times 5 \times 5 \times 1 \times 2$ $\text{LCM} = 6 \times 25 \times 2$ $\text{LCM} = 150 \times 2$ $\text{LCM} = 300$
The LCM of 150 and 300 is $\boxed{\text{300}}$ .

Find the LCM of 150 and 300 using the common division method.

Answer

Step-by-step solution

Divide 150 and 300 by a common prime factor, starting with 2.

Divide 75 and 150 by a common prime factor, which is 3.

Divide 25 and 50 by a common prime factor, which is 5.

Divide 5 and 10 by a common prime factor, which is 5.

The remaining numbers, 1 and 2, have no common prime factors other than 1.

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