Question 662412
Divide and conquer:
 
A common multiple of {{{50x^5y}}}, {{{60x^4y^3}}}, and {{{30x^2y^4}}}
has to be a multiple of {{{50=2*5*5}}}, {{{60=2*2*3*5}}}, and {{{30=2*3*5}}}
The LCM of those 3 coefficients is {{{2*2*3*5*5=300}}}.
 
A common multiple of {{{50x^5y}}}, {{{60x^4y^3}}}, and {{{30x^2y^4}}}
has to be a multiple of {{{x^5}}}, {{{x^4}}}, and {{{x^2}}}.
The LCM of those powers of {{{x}}} is obviously {{{x^5}}}, which is
a multiple of itself,
a multiple of {{{x^4}}}, because {{{x^5=(x^4)*x}}},
and a multiple of {{{x^2}}}, because {{{x^5=(x^2)*(x^3)}}}.
 
A common multiple of {{{50x^5y}}}, {{{60x^4y^3}}}, and {{{30x^2y^4}}}
has to be a multiple of {{{y}}}, {{{y^3}}}, and {{{y^4}}}.
The LCM of those powers of {{{y}}} is obviously {{{y^4}}}
 
The LCM of {{{50x^5y}}}, {{{60x^4y^3}}}, and {{{30x^2y^4}}} is
{{{highlight(300x^5y^4)}}}.