what is the lowest common denominator of 2/32 plus 4/28
32 = 2x2x2x2x2
28 =2x2x7
so LCD = 2x2x2x2x2x7 = 224
btw, both of your fractions would have been reduced first to 1/16 and 1/7 with a LCD of 112
To find the lowest common denominator (LCD) of two fractions, you need to find the smallest number that can be evenly divided by all the denominators involved. In this case, the denominators are 32 and 28.
Step 1: Prime factorize each denominator.
- The prime factorization of 32 is 2^5.
- The prime factorization of 28 is 2^2 × 7.
Step 2: Determine the highest power of each prime factor.
- The highest power of 2 is 5.
- The highest power of 7 is 1 (since it only appears in the prime factorization of 28).
Step 3: Calculate the LCD.
- The LCD is the product of the highest powers of each prime factor: 2^5 × 7 = 224.
So, the lowest common denominator (LCD) of 2/32 and 4/28 is 224.