The sum of L.C.M and H.C.F of two numbers is 590. If L.C.M is 580 more than the H.C.F and one of the numbers is 45, find the other number.

Sure, here are the steps to solve the problem:

Step 1: According to the problem, the sum of L.C.M and H.C.F is 590. So, we can write it as: L.C.M + H.C.F = 590

Step 2: It is also given that L.C.M is 580 more than the H.C.F. So, we can write it as: L.C.M = H.C.F + 580

Step 3: Now, substitute the value of L.C.M from equation 2 into equation 1: H.C.F + 580 + H.C.F = 590 2H.C.F = 590 - 580 2H.C.F = 10 H.C.F = 10 / 2 H.C.F = 5

Step 4: Substitute the value of H.C.F into equation 2 to find the L.C.M: L.C.M = 5 + 580 L.C.M = 585

Step 5: Now, we know that the product of two numbers is equal to the product of their L.C.M and H.C.F. So, we can write it as: First number * Second number = L.C.M * H.C.F

Step 6: Substitute the given values into the equation: 45 * Second number = 585 * 5 Second number = (585 * 5) / 45 Second number = 65

So, the other number is 65.