What is the shortest length of television cable that
could be cut into either a whole number of 18-ft pieces
or a whole number of 30-ft pieces?
u should of learned that in school ahh
The answer is 90.
To find the shortest length of television cable that could be cut into either a whole number of 18-ft pieces or a whole number of 30-ft pieces, we need to find the least common multiple (LCM) of 18 and 30.
Step 1: Find the prime factorization of both numbers:
- The prime factorization of 18 is 2 * 3^2.
- The prime factorization of 30 is 2 * 3 * 5.
Step 2: Take the highest exponent for each prime factor:
- The highest exponent of 2 is 1.
- The highest exponent of 3 is 2.
- The highest exponent of 5 is 1.
Step 3: Multiply the prime factors with their highest exponents:
2^1 * 3^2 * 5^1 = 2 * 9 * 5 = 90.
Therefore, the LCM of 18 and 30 is 90.
Hence, the shortest length of television cable that could be cut into either a whole number of 18-ft pieces or a whole number of 30-ft pieces is 90 feet.
To find the shortest length of television cable that can be cut into either a whole number of 18-ft pieces or a whole number of 30-ft pieces, you need to find the least common multiple (LCM) of 18 and 30.
To determine the LCM, you can start by listing the multiples of each number and finding the first common multiple:
Multiples of 18: 18, 36, 54, 72, ...
Multiples of 30: 30, 60, 90, ...
The first common multiple is 90, which means that the shortest length of cable that can be cut into either a whole number of 18-ft pieces or 30-ft pieces is 90 ft.