What Is the LCM of 17 and 31?
The LCM of 17 and 31 is 527. It is the smallest number that both 17 and 31 divide into evenly, which makes it the first multiple the two numbers share.
Method 1: List the Multiples
Write the multiples of each number until the lists meet.
- 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 LCM(17, 31) = 527.
Method 2: Use Prime Factorization
Write each number as primes, then take every prime that shows up, at its highest power.
- 17 = 17
- 31 = 31
Highest powers of every prime: 17 × 31 = 527.
Method 3: Use the GCF
The GCF of 17 and 31 is 1. The LCM is the product divided by the GCF:
(17 × 31) ÷ 1 = 527 ÷ 1 = 527
Because the GCF is 1, the numbers are coprime and the LCM is simply their product.
Check the Answer
527 ÷ 17 = 31 and 527 ÷ 31 = 17. Both are whole numbers, and no smaller number works for both, so 527 is the least common multiple.
Add Fractions with the LCM
The LCM is the least common denominator. To add 1/17 + 1/31, rewrite both over 527:
1/17 + 1/31 = 31/527 + 17/527 = 48/527
Want a different pair? Use the LCM Calculator.