What Is the LCD of 48 and 180?
The least common denominator of 48 and 180 is 720. It is the smallest number that both denominators divide into evenly, which is the same number as the least common multiple of 48 and 180.
Method 1: List the Multiples
- 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 the LCD is 720.
Method 2: Use Prime Factorization
- 48 = 2⁴ × 3
- 180 = 2² × 3² × 5
Take every prime at its highest power: 2⁴ × 3² × 5 = 720.
Method 3: Use the GCF
The GCF of 48 and 180 is 12, so the LCD is the product divided by the GCF:
(48 × 180) ÷ 12 = 8,640 ÷ 12 = 720
Rewrite the Fractions over 720
Multiply the top and bottom of each fraction so the denominator becomes 720:
- 1/48 = (1 × 15)/(48 × 15) = 15/720
- 1/180 = (1 × 4)/(180 × 4) = 4/720
Now the denominators match, so you can add or compare them: 1/48 + 1/180 = 19/720.
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