Two sizes of concrete blocks are being used to build a raised garden bed for strawberries the first kind of block is 8 inches long and the second is 12 inches long a row of the shorter block is laid on the top of row of the longer blocks using only whole blocks what is the shortest length for which the two rows of blocks are equally long
What is the least common multiple of 8 and 12?
24
Yes.
To find the shortest length for which the two rows of blocks are equally long, we need to find the common multiple of the lengths of the two block sizes.
The first kind of block is 8 inches long, and the second kind is 12 inches long.
To find the common multiple, we can use the concept of the least common multiple (LCM).
The LCM is the smallest multiple that is divisible by both numbers.
The prime factorization of 8 is 2^3, and the prime factorization of 12 is 2^2 * 3.
To find the LCM, we take the highest power of each prime factor that occurs in either factorization: 2^3 * 3 = 24.
Therefore, the least common multiple (LCM) of 8 and 12 is 24 inches.
So, the two rows of blocks would be equally long at a length of 24 inches.