F.4 Maths

Consider the HCF, for the constant part of the monomial, the power of 2 is 1, the power of 3 is not important…(1)
The power of a is at least 2 …(2)
The power of b is 1…(3)
The power of c is at least 1…(4)
Consider the LCM, for the constant part of the monomial, the power of 3 is 2, the power of 2 is at most 3…(5)
The power of a is at most 3 …(6)
The power of b is at most 3…(7)
The power of c is 2…(8)
(1) & (5) => Constant part if (2^1)(3^2) = 18
(2) & (6) => power of a is 2 or 3
(3) & (7) => power of b is 1
(4) & (8) => power of c is 2
The monomial can be 18a^2bc^2 or 18a^3bc^2