The L.C.M of two numbers is 900. Which of these numbers 300, 100, 200 and 50 cannot be the H.C.F?

The Highest Common Factor (H.C.F) of two numbers is the largest number that divides both of them without leaving a remainder. The Lowest Common Multiple (L.C.M) of two numbers is the smallest number that is a multiple of both of them.

Given that the L.C.M of the two numbers is 900, we need to find out which of the numbers 300, 100, 200, and 50 cannot be the H.C.F.

The H.C.F of two numbers must always be a factor of their L.C.M. Therefore, to find out which of the numbers cannot be the H.C.F, we need to check which of them are not factors of 900.

1. 300: 900 divided by 300 equals 3, so 300 is a factor of 900.
2. 100: 900 divided by 100 equals 9, so 100 is a factor of 900.
3. 200: 900 divided by 200 equals 4.5, so 200 is not a factor of 900.
4. 50: 900 divided by 50 equals 18, so 50 is a factor of 900.

Therefore, out of the numbers 300, 100, 200, and 50, the number 200 cannot be the H.C.F of the two numbers.