The LCM of 64, 82 and k is 124 where k is a positive integer. Find the smallest value of k. Showyour steps

Sure, here are the steps to find the smallest value of k:

Step 1: Find the LCM of 64 and 82.

The prime factorization of 64 is 2^6 and of 82 is 2 * 41. The LCM is found by multiplying the highest power of all prime numbers in the numbers' factorization. So, the LCM of 64 and 82 is 2^6 * 41 = 2624.

Step 2: Compare the LCM of 64 and 82 with the given LCM.

The LCM of 64, 82 and k is given as 124. But the LCM of 64 and 82 that we calculated is 2624, which is greater than 124. This is a contradiction, because the LCM of three numbers cannot be less than the LCM of any two of those numbers.

Therefore, there seems to be a mistake in the problem as it is not possible to find a positive integer k that would make the LCM of 64, 82 and k equal to 124.