Question

The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 5 : 4. What are the 2 numbers?​

Answer 1

To find the two numbers, use the concept of least common multiple (LCM) and the given ratio. The two numbers are 200 and 160.

Step-by-step explanation:

To find the two numbers, we can use the concept of least common multiple (LCM) and the given ratio. Let's say the two numbers are x and y. We are told that the LCM of x and y is 40. This means that 40 is a multiple of both x and y. Additionally, we are given that the ratio of the greater number to the lesser number is 5:4, which means x/y = 5/4.

Since the LCM of x and y is 40, we can write two equations:

x = 40a, where a is a positive integer, because x is a multiple of 40.

y = 40b, where b is a positive integer, because y is a multiple of 40.

Substituting these values into the ratio equation, we get (40a)/(40b) = 5/4. Simplifying this equation gives us a/b = 5/4.

Since a/b = 5/4, we need to find integers a and b that satisfy this condition. The lowest values for which this is true are a = 5 and b = 4.

Therefore, the two numbers are x = 40a = 40(5) = 200 and y = 40b = 40(4) = 160.

Answer 2

10 and 8

Step-by-step explanation:

must be in the ratio 5:4, 5 x 4 =20, so if you multiply by 2 the ratio is 10:8 (same thing). The least common multiple of 10 and 8 is 40 because you can do 10 x 4 = 40 and 8 x 5 = 40.