The L.C.M of two numbers is 560 and their ratio is 4:5. Find the two numbers

Step 1: The ratio of the two numbers is given as 4:5. Let's assume the two numbers as 4x and 5x.

Step 2: The L.C.M of two numbers is the product of the numbers divided by their H.C.F. Since the numbers are in ratio and we have assumed them as 4x and 5x, their H.C.F will be x.

So, according to the problem, L.C.M = (4x * 5x) / x

Step 3: Substituting the given L.C.M (560) in the above equation, we get 560 = (4x * 5x) / x

Step 4: Simplifying the equation, we get 560 = 20x

Step 5: Solving for x, we get x = 560 / 20 = 28

Step 6: Substituting x = 28 in 4x and 5x, we get the two numbers as 428 = 112 and 528 = 140.

So, the two numbers are 112 and 140.