find a common denominater for the following fractions
3/4, 63/111, 59/122, 15/29, 44/71, 12/23, 7/10,1/2 and 12/19
a common denominator, not the lowest is ...
2*111*122*29*71*23*10*12*19
i meant for all the fractions so we can find equivalent fraction
To find a common denominator for the given fractions, we need to determine the least common multiple (LCM) of the denominators.
1. Start by listing the prime factors of each denominator:
- Denominator of 3/4: 4 = 2^2
- Denominator of 63/111: 111 = 3 * 37
- Denominator of 59/122: 122 = 2 * 61
- Denominator of 15/29: 29 = 29
- Denominator of 44/71: 71 = 71
- Denominator of 12/23: 23 = 23
- Denominator of 7/10: 10 = 2 * 5
- Denominator of 1/2: 2 = 2
- Denominator of 12/19: 19 = 19
2. Next, determine the highest power of each prime factor that appears in any denominator.
- 2: maximum power is 2
- 3: maximum power is 1
- 5: maximum power is 1
- 7: maximum power is 1
- 11: maximum power is 1
- 13: maximum power is 1
- 17: maximum power is 1
- 19: maximum power is 1
- 23: maximum power is 1
- 29: maximum power is 1
- 37: maximum power is 1
- 41: maximum power is 1
- 43: maximum power is 1
- 47: maximum power is 1
- 53: maximum power is 1
- 59: maximum power is 1
- 61: maximum power is 1
- 67: maximum power is 1
- 71: maximum power is 1
3. Multiply all the prime factors raised to their corresponding highest powers.
LCM = 2^2 * 3 * 5 * 7 * 11 * 13 * 17 * 19 * 23 * 29 * 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71
4. Simplify the LCM if necessary.
Using a calculator or a computer algebra system is the easiest way to compute this large LCM value. The resulting LCM will be a common denominator for all the given fractions.