Leah has two same size rectangles divided into the same number of Equal parts. One rectangle has 1/3 of the parts shaded and the other has 2/5 of the parts shaded. What is the least number of parts into which both rectangles can be divide?
Find the least common multiple (LCM) of 3 and 5 which is?
To determine the least number of parts into which both rectangles can be divided, we need to find the least common multiple (LCM) of the denominators 3 and 5 (since 1/3 and 2/5 are the shaded parts of the rectangles, respectively).
To find the LCM of 3 and 5:
1. Determine the prime factors of each number:
- 3 is a prime number, so its prime factorization is just 3.
- 5 is also a prime number, so its prime factorization is just 5.
2. Find the highest power of each prime factor that appears in either number:
- The highest power of 3 that appears is 3^1 (since 3 is only a factor of 3 once).
- The highest power of 5 that appears is 5^1 (since 5 is only a factor of 5 once).
3. Multiply the highest powers of the prime factors together:
- LCM = 3^1 * 5^1 = 3 * 5 = 15.
Therefore, the least number of parts into which both rectangles can be divided is 15.