What Is the LCM of 24 and 36?
The LCM of 24 and 36 is 72. It is the smallest number that both 24 and 36 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 24: 24, 48, 72
- Multiples of 36: 36, 72
The first number in both lists is 72, so LCM(24, 36) = 72.
Method 2: Use Prime Factorization
Write each number as primes, then take every prime that shows up, at its highest power.
- 24 = 2³ × 3
- 36 = 2² × 3²
Highest powers of every prime: 2³ × 3² = 72.
Method 3: Use the GCF
The GCF of 24 and 36 is 12. The LCM is the product divided by the GCF:
(24 × 36) ÷ 12 = 864 ÷ 12 = 72
Dividing first keeps the numbers small: 24 ÷ 12 = 2, and 2 × 36 = 72.
Check the Answer
72 ÷ 24 = 3 and 72 ÷ 36 = 2. Both are whole numbers, and no smaller number works for both, so 72 is the least common multiple.
Add Fractions with the LCM
The LCM is the least common denominator. To add 1/24 + 1/36, rewrite both over 72:
1/24 + 1/36 = 3/72 + 2/72 = 5/72
Want a different pair? Use the LCM Calculator.