Question

If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then find the product of two numbers.

A. 900
B. 600
C. 450
D. 300

Answer 1

The two numbers are 1080 and 180, and their product is 194,400.

Step-by-step explanation:

Let's assume the two numbers are x and y.

According to the given information, we have:

LCM(x, y) + HCF(x, y) = 1260

LCM(x, y) = HCF(x, y) + 900

Using these equations, we can solve for x and y.

Let's express the HCF in terms of x and y.

HCF(x, y) = LCM(x, y) - 900

Substituting this into the first equation, we get:

LCM(x, y) + LCM(x, y) - 900 = 1260

2 * LCM(x, y) = 2160

LCM(x, y) = 1080

Now we can substitute this value back into the second equation and solve for x and y:

1080 = LCM(x, y) = HCF(x, y) + 900

1080 - 900 = HCF(x, y)

HCF(x, y) = 180

Therefore, the two numbers are 1080 and 180, and their product is 1080 * 180 = 194,400.