let

x = the age of Marcy

y = the age of Tracy

z = the age of Lacy

Marcy is the youngest thus x<y and x<z

Tracy is a year older than Marcy

y = x + 1

Lacy is two years older than Marcy

z = x + 2

when their ages are multiplied, the result is 1716

x*y*z = 1716 or

x*(x + 1)*(x + 2) = 1716

by solving the cubic equation we find one real solution and 2 complex

we consider the real solution that is x = 11 years

y = 11 + 1 = 12 years

z = 11 + 2 = 13 years

Marcy is 11 years old.

Tracy is 12 years old.

Lacy is 13 years old.