write the LCD for each pair4/7, 1/8, 11/12
So if by LCD you mean Least Common Denominator, I would start off with finding values of 7 8 12 that are the same, so by multiplying 7 and 8 you get 56 which is not a multiple of 12.
so we must now find the LCM of 56 and 12 which is 168 found by looking at the progression of numbers 56..112...168 and 12..24..36..48..60..72..and so on.
so to sum up LCM is 168 for all three numbers.56 for 7 and 8. 72 for 12 and 8. or 84 for 7 and 12.
7 = 1x7
8 = 2x2x2
12 = 2x2x3
Everybody must be represented, so
LCD = 1x2x2x2x3x7 = 168
To find the least common denominator (LCD) for each pair, we need to determine the smallest common multiple of the denominators.
For the first pair, the denominators are 7 and 8. To find the least common multiple (LCM) of these numbers, we can list their multiples and find the smallest common one:
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
The first common multiple of both 7 and 8 is 56. Hence, the LCD for 4/7 and 1/8 is 56.
For the second pair, the denominators are 8 and 12. Again, we can list their multiples and find the smallest common one:
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, ...
The first common multiple of both 8 and 12 is 24. Therefore, the LCD for 1/8 and 11/12 is 24.
In summary:
- The LCD for 4/7 and 1/8 is 56.
- The LCD for 1/8 and 11/12 is 24.