Solve (4+x^2)*(7+x^3),(11+x^5),(16+x^8)

$$( 4 + x ^ { 2 } ) \cdot ( 7 + x ^ { 3 } ) , ( 11 + x ^ { 5 } ) , ( 16 + x ^ { 8 } )$$

Least Common Multiple

$$\left(x^{2}+4\right)\left(x^{3}+7\right)\left(x^{5}+11\right)\left(x^{8}+16\right)$$

Solution Steps

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

$$\left(x^{2}+4\right)\left(x^{3}+7\right)\left(x^{5}+11\right)\left(x^{8}+16\right)$$

Expand the expression.

$$x^{18}+4x^{16}+7x^{15}+39x^{13}+44x^{11}+93x^{10}+372x^{8}+112x^{7}+624x^{5}+704x^{3}+1232x^{2}+4928$$

Evaluate

$$\left(x^{2}+4\right)\left(x^{3}+7\right),x^{5}+11,x^{8}+16$$