What Is the LCD of 24 and 36?
The least common denominator of 24 and 36 is 72. It is the smallest number that both denominators divide into evenly, which is the same number as the least common multiple of 24 and 36.
Method 1: List the Multiples
- Multiples of 24: 24, 48, 72
- Multiples of 36: 36, 72
The first number in both lists is 72, so the LCD is 72.
Method 2: Use Prime Factorization
- 24 = 2³ × 3
- 36 = 2² × 3²
Take every prime at its highest power: 2³ × 3² = 72.
Method 3: Use the GCF
The GCF of 24 and 36 is 12, so the LCD is the product divided by the GCF:
(24 × 36) ÷ 12 = 864 ÷ 12 = 72
Rewrite the Fractions over 72
Multiply the top and bottom of each fraction so the denominator becomes 72:
- 1/24 = (1 × 3)/(24 × 3) = 3/72
- 1/36 = (1 × 2)/(36 × 2) = 2/72
Now the denominators match, so you can add or compare them: 1/24 + 1/36 = 5/72.
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