Three numbers have a ratio of 3:4:5, and their least common multiple (LCM) is 2400. What is their highest common factor (HCF)?

Explanation

Let the three numbers be 3x, 4x, and 5x. The LCM of these numbers is the product of the highest multiple, which is 60x. Given that 60x = 2400, solving for x gives x = 40. Therefore, the numbers are 120, 160, and 200. The HCF of these numbers is the value of x, which is 40.