Solve {l}{text{(A)}100,150,200}{text{(8)}200,360,160}{text{(C)}160,360,200}{text{(D)}360,160,200}

$$\left. \begin{array} { l } { \text { (A) } 100,150,200 } \\ { \text { (8) } 200,360,160 } \\ { \text { (C) } 160,360,200 } \\ { \text { (D) } 360,160,200 } \end{array} \right.$$

Least Common Multiple

$$14400ACD$$

Solution Steps

Factor the expressions that are not already factored.

$$150=2\times 3\times 5^{2} 200=2^{3}\times 5^{2} 1600=2^{6}\times 5^{2} 360=2^{3}\times 3^{2}\times 5 160=2^{5}\times 5 360=2^{3}\times 3^{2}\times 5 200=2^{3}\times 5^{2} 160=2^{5}\times 5 200=2^{3}\times 5^{2}$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$14400ACD$$

Evaluate

$$100A,\ 150,\ 200,\ 1600,\ 360,\ 160,\ 160C,\ 360,\ 200,\ 360D,\ 160,\ 200$$