Solve l^{2}+m^{2},m^2+n^2,n^2+l^2

$$l ^ { 2 } + m ^ { 2 } , m ^ { 2 } + n ^ { 2 } , n ^ { 2 } + l ^ { 2 }$$

Least Common Multiple

$$\left(m^{2}+l^{2}\right)\left(n^{2}+l^{2}\right)\left(m^{2}+n^{2}\right)$$

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.

$$\left(m^{2}+l^{2}\right)\left(n^{2}+l^{2}\right)\left(m^{2}+n^{2}\right)$$

Expand the expression.

$$l^{2}m^{4}+m^{2}n^{4}+2l^{2}m^{2}n^{2}+m^{2}l^{4}+l^{2}n^{4}+n^{2}m^{4}+n^{2}l^{4}$$

Evaluate

$$m^{2}+l^{2},m^{2}+n^{2},n^{2}+l^{2}$$