the shortest length of fabric that can be divided exactly into equal parts of length 9 m, 12m, 36m or 48m
I meant find theshortest•••
What is the least common multiple of these numbers?
To find the shortest length of fabric that can be divided exactly into equal parts of length 9m, 12m, 36m, or 48m, we need to find the least common multiple (LCM) of these lengths.
Here is the step-by-step process to find the LCM:
1. Prime factorize each of the given lengths:
- 9m = 3^2 * 1
- 12m = 2^2 * 3^1
- 36m = 2^2 * 3^2
- 48m = 2^4 * 3^1
2. Identify the highest exponent of each prime factor from the prime factorization of each length.
- The highest exponent of 2 is 4 (from 48m).
- The highest exponent of 3 is 2 (from 36m).
- The highest exponent of each other prime factor is 0.
3. Multiply the prime factors with their respective highest exponents to find the LCM:
LCM = 2^4 * 3^2 = 16 * 9 = 144m
Therefore, the shortest length of fabric that can be divided exactly into equal parts of length 9m, 12m, 36m, or 48m is 144m.