L.C.M of 3 different number is 256. which one of the following can never be…

To solve this problem, we must understand a fundamental property of the relationship between the Least Common Multiple (L.C.M.) and the Highest Common Factor (H.C.F.) of any set of numbers:

The H.C.F. of a set of numbers must always be a divisor (factor) of their L.C.M.

In other words, if you divide the L.C.M. by the H.C.F., the result must be an integer with no remainder.

Step-by-Step Analysis
Given L.C.M.: 256

Evaluate the options to see which one is NOT a divisor of 256:

Option A: 4
256 / 4 = 64. Since this is an integer, 4 can be an H.C.F.

Option B: 16
256 / 16 = 16. Since this is an integer, 16 can be an H.C.F.

Option C: 24
256 / 24 = 10.66... Since this is not an integer, 24 cannot be a divisor of 256. Therefore, it cannot be the H.C.F.

Option D: 32
256 / 32 = 8. Since this is an integer, 32 can be an H.C.F.