What Is the LCD of 17 and 31?
The least common denominator of 17 and 31 is 527. It is the smallest number that both denominators divide into evenly, which is the same number as the least common multiple of 17 and 31.
Method 1: List the Multiples
- Multiples of 17: 17, 34, 51, 68, 85, 102, … , 527
- Multiples of 31: 31, 62, 93, 124, 155, 186, … , 527
The first number in both lists is 527, so the LCD is 527.
Method 2: Use Prime Factorization
- 17 = 17
- 31 = 31
Take every prime at its highest power: 17 × 31 = 527.
Method 3: Use the GCF
The GCF of 17 and 31 is 1, so the LCD is the product divided by the GCF:
(17 × 31) ÷ 1 = 527 ÷ 1 = 527
Rewrite the Fractions over 527
Multiply the top and bottom of each fraction so the denominator becomes 527:
- 1/17 = (1 × 31)/(17 × 31) = 31/527
- 1/31 = (1 × 17)/(31 × 17) = 17/527
Now the denominators match, so you can add or compare them: 1/17 + 1/31 = 48/527.
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