What Is the LCM of 48 and 180?
The LCM of 48 and 180 is 720. It is the smallest number that both 48 and 180 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 48: 48, 96, 144, 192, 240, 288, … , 720
- Multiples of 180: 180, 360, 540, 720
The first number in both lists is 720, so LCM(48, 180) = 720.
Method 2: Use Prime Factorization
Write each number as primes, then take every prime that shows up, at its highest power.
- 48 = 2⁴ × 3
- 180 = 2² × 3² × 5
Highest powers of every prime: 2⁴ × 3² × 5 = 720.
Method 3: Use the GCF
The GCF of 48 and 180 is 12. The LCM is the product divided by the GCF:
(48 × 180) ÷ 12 = 8,640 ÷ 12 = 720
Dividing first keeps the numbers small: 48 ÷ 12 = 4, and 4 × 180 = 720.
Check the Answer
720 ÷ 48 = 15 and 720 ÷ 180 = 4. Both are whole numbers, and no smaller number works for both, so 720 is the least common multiple.
Add Fractions with the LCM
The LCM is the least common denominator. To add 1/48 + 1/180, rewrite both over 720:
1/48 + 1/180 = 15/720 + 4/720 = 19/720
Want a different pair? Use the LCM Calculator.