Find the least common multiple of 20, 30, and 50.
Factor each one into their primary factors 5 & 2 & 2, 2 & 3 & 5, and finally 2 & 5 & 5.
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Another way to solve this problem is to list each of the multiples:
20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360
30, 60, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360
50, 100, 150, 200, 250, 300, 350
What is the smallest number that's the same on all three lists?
To find the least common multiple (LCM) of 20, 30, and 50, we can follow these steps:
1. Write down the prime factorizations of each number:
- 20: 2 * 2 * 5
- 30: 2 * 3 * 5
- 50: 2 * 5 * 5
2. Identify the highest exponent for each prime factor by comparing the factorizations:
- The highest exponent of 2 is 2 (from 20 and 50).
- The highest exponent of 3 is 1 (from 30).
- The highest exponent of 5 is 2 (from all three numbers).
3. Multiply the prime factors raised to their highest exponents:
2^2 * 3^1 * 5^2 = 4 * 3 * 25 = 300.
Therefore, the LCM of 20, 30, and 50 is 300.