Find the LCM of a^5+a^4+1 and a^5+a+1

First let us find the GCD

GCD ( a^5+ a^ 4+ 1, a^5 + a + 1)
= GCD( a^5 + a + 1, a^4- a) using GCD(a,b) = gcd(b , a -b)
= GCD(a^5+ a+ 1 , a^3(a-1))
= GCD(a^5+ a + 1, a- 1) as a is coprime to a^5 + a + 1
= 1 as a-1 is not a factor of a^5 + a + 1

so a^5+a^4+1 and a^5+a+1 are copimes

so LCM = product = (a^5+a^4+1)(a^5+ a+ 1)