Step-by-step explanation:
let's use the prime factor approach :
180 = 2×2×3×3×5
189 = 3×3×3×7
600 = 2×2×2×3×5×5
what is the longest and highest combination of prime factors they have in common ?
180 and 189 have at least 3×3 = 9 in common. the 2, 5 and 7 appear only in one of the numbers.
but 600 "supports" only one of these 3s.
so that the highest common factor (hcm) for all 3 numbers = 3
