Answer :
To find the least common denominator of the fractions [tex]\(\frac{2}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex], we need to determine the least common multiple (LCM) of the denominators 7 and 5.
Step-by-Step Solution:
1. Identify the denominators:
- The denominators are 7 and 5.
2. Find the prime factors:
- 7 is already a prime number: 7
- 5 is already a prime number: 5
3. Calculate the least common multiple (LCM):
- The LCM is the smallest number that both denominators can divide into without leaving a remainder.
- Since 7 and 5 have no common factors other than 1, we simply multiply these denominators together.
[tex]\[ \text{LCM}(7, 5) = 7 \times 5 = 35 \][/tex]
Thus, the least common denominator for the fractions [tex]\(\frac{2}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] is:
[tex]\[ \boxed{35} \][/tex]
Step-by-Step Solution:
1. Identify the denominators:
- The denominators are 7 and 5.
2. Find the prime factors:
- 7 is already a prime number: 7
- 5 is already a prime number: 5
3. Calculate the least common multiple (LCM):
- The LCM is the smallest number that both denominators can divide into without leaving a remainder.
- Since 7 and 5 have no common factors other than 1, we simply multiply these denominators together.
[tex]\[ \text{LCM}(7, 5) = 7 \times 5 = 35 \][/tex]
Thus, the least common denominator for the fractions [tex]\(\frac{2}{7}\)[/tex] and [tex]\(\frac{2}{5}\)[/tex] is:
[tex]\[ \boxed{35} \][/tex]
