Solve {l}{text{A}30,18,16,20,18,28,18}{text{B}32,10,33,43,12,33,12}{text{C}18,12,11,10,22,40,45}{text{D}4,30,16,35,17,19,19}

$$\left. \begin{array} { l } { \text { A } 30,18,16,20,18,28,18 } \\ { \text { B } 32,10,33,43,12,33,12 } \\ { \text { C } 18,12,11,10,22,40,45 } \\ { \text { D } 4,30,16,35,17,19,19 } \end{array} \right.$$

Least Common Multiple

$$1540012320ABCD$$

Solution Steps

Factor the expressions that are not already factored.

$$18=2\times 3^{2} 16=2^{4} 20=2^{2}\times 5 18=2\times 3^{2} 28=2^{2}\times 7 18=2\times 3^{2} 10=2\times 5 33=3\times 11 12=2^{2}\times 3 33=3\times 11 12=2^{2}\times 3 12=2^{2}\times 3 10=2\times 5 22=2\times 11 40=2^{3}\times 5 45=3^{2}\times 5 30=2\times 3\times 5 16=2^{4} 35=5\times 7$$

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

$$1540012320ABCD$$

Evaluate

$$30A,\ 18,\ 16,\ 20,\ 18,\ 28,\ 18,\ 32B,\ 10,\ 33,\ 43,\ 12,\ 33,\ 12,\ 18C,\ 12,\ 11,\ 10,\ 22,\ 40,\ 45,\ 4D,\ 30,\ 16,\ 35,\ 17,\ 19,\ 19$$