Find the LCD for the following pair of fractions.
1/10 and 16/45
the least common denominator is ___.
To find the least common denominator (LCD) for the pair of fractions 1/10 and 16/45, we need to find the least common multiple (LCM) of the denominators, which are 10 and 45.
The prime factorization of 10 is 2 × 5.
The prime factorization of 45 is 3² × 5.
To find the LCM, we take the highest power of each prime factor that appears in either prime factorization.
Hence, the LCM (and LCD) of 10 and 45 is 2 × 3² × 5 = 90.
Therefore, the least common denominator is 90.
To find the least common denominator (LCD) for the fractions 1/10 and 16/45, we need to find the least common multiple (LCM) of the denominators 10 and 45.
To find the LCM, we can list the multiples of each denominator until we find a common multiple.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
We can see that the least common multiple of 10 and 45 is 90.
Therefore, the LCD for the fractions 1/10 and 16/45 is 90.
To find the least common denominator (LCD) for a pair of fractions, we need to find the least common multiple (LCM) of their denominators. Here's how you can find the LCD for the fractions 1/10 and 16/45:
Step 1: Find the LCM of the denominators (10 and 45).
- Start by listing the multiples of each denominator.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, ...
Step 2: Find the smallest number that appears in both lists.
- In this case, the smallest number that appears in both lists is 90.
Step 3: The LCD is the smallest number found in Step 2.
- Therefore, the LCD for 1/10 and 16/45 is 90.
So, the least common denominator for the fractions 1/10 and 16/45 is 90.