Step-by-step explanation:
hcm is the highest common factor, also know as the gates common divisor.
in other words, what is the biggest expression that divides all given terms without remainder ?
3 divides 24 and 30. that is fine.
every term has one p and at least one r. only 2 out of the 3 terms have a q (so that is not part of it).
therefore, the hcm or gcd is 3pr
lcm is the lowest common multiple.
that means, what is the smallest expression that can be divided by all 3 terms without remainder ?
let's start with the numbers and use the prime factor approach :
3 = 3
24 = 2×2×2×3
30 = 2×3×5
lcm of these 3 numbers is then the combination of the longest streaks of the various prime factors :
2×2×2×3×5 = 120
about the variables
pq²r² can be divided by pqr and also by pr². and, of course, by pq²r² itself too.
so, we don't need to "add" anything.
so, the lcm is 120pq²r²
