Find the least number exactly divisible by 12, 15, 20 and 27.
Question
Find the least number exactly divisible by 12, 15, 20 and 27.
Solution
To find the least number exactly divisible by 12, 15, 20, and 27, we need to find the least common multiple (LCM) of these numbers.
Step 1: Prime factorize each number:
- 12 = 2^2 * 3
- 15 = 3 * 5
- 20 = 2^2 * 5
- 27 = 3^3
Step 2: Identify the highest power of each prime factor:
- The highest power of 2 is 2^2.
- The highest power of 3 is 3^3.
- The highest power of 5 is 5.
Step 3: Multiply the highest powers of each prime factor: 2^2 * 3^3 * 5 = 4 * 27 * 5 = 540
Therefore, the least number exactly divisible by 12, 15, 20, and 27 is 540.
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