Solve {l}{text{(a)}35^{circ},48^{circ},120^{circ}}{text{(b)}30^{circ},65^{circ},150^{circ}}{text{(c)}29^{circ},108^{circ},65^circ}{text{(d)}23^circ,78^circ,99^circ}

$$\left. \begin{array} { l } { \text { (a) } 35 ^ { \circ } , 48 ^ { \circ } , 120 ^ { \circ } } \\ { \text { (b) } 30 ^ { \circ } , 65 ^ { \circ } , 150 ^ { \circ } } \\ { \text { (c) } 29 ^ { \circ } , 108 ^ { \circ } , 65 ^ { \circ } } \\ { \text { (d) } 23 ^ { \circ } , 78 ^ { \circ } , 99 ^ { \circ } } \end{array} \right.$$

Least Common Multiple

$$7210803600abcd$$

Solution Steps

Factor the expressions that are not already factored.

$$48=2^{4}\times 3 120=2^{3}\times 3\times 5 65=5\times 13 150=2\times 3\times 5^{2} 108=2^{2}\times 3^{3} 65=5\times 13 78=2\times 3\times 13 99=3^{2}\times 11$$

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

$$7210803600abcd$$

Evaluate

$$35a,\ 48,\ 120,\ 30b,\ 65,\ 150,\ 29c,\ 108,\ 65,\ 23d,\ 78,\ 99$$