Answer: 1080
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Step-by-step explanation:
Write out the prime factorization of each value. A factor tree may help.
- 72 = 2^3*3^2
- 216 = 2^3*3^3
- 270 = 2*3^2*5
The unique primes that show up are: 2, 3, 5
- For the prime factor 2, the highest exponent is 3. So 2^3 is a factor of the LCM.
- For the prime factor 3, the highest exponent is 3. So 3^3 is a factor of the LCM.
- For the prime factor 5, the highest exponent is 1. So 5^1 is a factor of the LCM
The LCM is 2^3*3^3*5^1 = 8*27*5 = 1080