What Is the LCM of 84 and 126?
The LCM of 84 and 126 is 252. It is the smallest number that both 84 and 126 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 84: 84, 168, 252
- Multiples of 126: 126, 252
The first number in both lists is 252, so LCM(84, 126) = 252.
Method 2: Use Prime Factorization
Write each number as primes, then take every prime that shows up, at its highest power.
- 84 = 2² × 3 × 7
- 126 = 2 × 3² × 7
Highest powers of every prime: 2² × 3² × 7 = 252.
Method 3: Use the GCF
The GCF of 84 and 126 is 42. The LCM is the product divided by the GCF:
(84 × 126) ÷ 42 = 10,584 ÷ 42 = 252
Dividing first keeps the numbers small: 84 ÷ 42 = 2, and 2 × 126 = 252.
Check the Answer
252 ÷ 84 = 3 and 252 ÷ 126 = 2. Both are whole numbers, and no smaller number works for both, so 252 is the least common multiple.
Add Fractions with the LCM
The LCM is the least common denominator. To add 1/84 + 1/126, rewrite both over 252:
1/84 + 1/126 = 3/252 + 2/252 = 5/252
Want a different pair? Use the LCM Calculator.