A least common denominator is the least common multiple of two or more denominators. Take the fractions and . The smallest number that evenly divides both 3 and 6 is 6. So 6 is the least common denominator of 3 and 6 is 6.
Step | Equation | Description |
---|---|---|
1 | 3 | Find all the prime factors of the first denominator. |
2 | 2·3 | Find all the prime factors of the second denominator. |
3 | 2·3 = 6 | Combine the prime factors of the two denominators. |
Table 1: Least common denominator of 3 and 6. |
Least common denominators are used when adding or subtracting fractions. Since two fractions can be added or subtracted only if they have the same denominator, the least common denominator is used to transform the fractions.
Step | Equation | Description |
---|---|---|
1 | This is the expression to simplify. | |
2 | Find all the prime factors of the first denominator. | |
3 | Find all the prime factors of the second denominator. | |
4 | Combine the prime factors of the two denominators. | |
5 | What number times 10 equals the least common denominator? | |
6 | What number times 12 equals the least common denominator? | |
7 | Transform the first fraction. | |
8 | Transform the second fraction. | |
9 | Perform the addition. | |
Table 3: Adding 3/10 and 5/12. |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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