LCM of 125, 235, 270
Factor each into primes:
125 = 5 * 5 * 5
235 = 5 * 47
270 = 2 * 3 * 3 * 3 * 5
The LCM is the product of the minimum list of primes needed to make all of those numbers (125, 235, 270).
For instance, there's a factor of 2 in 270, so the LCM has to have a factor of 2.
There are three 3's as factors in 270, so the LCM has to have a factor of three 3's.
There are three 5's as factors in 125, so the LCM has to have a factor of three 5's. There's a 5 in 235, but that's already covered by one of the three 5's.
There's a 47 in 235, so the LCM has to have a factor of 47.
Basically you start with this:
125 = 5 * 5 * 5
235 = 5 * 47
270 = 2 * 3 * 3 * 3 * 5
Then make a list like this:
2 * 3 * 3 * 3 * 5 * 5 * 5 * 27
Then multiply it together like this:
2 * 3 * 3 * 3 * 5 * 5 * 5 * 27 = 182250
Answer: The LCM of 125, 235, and 270 is 182250
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GCF of 125, 235, and 270
Start with a list of primes:
125 = 5 * 5 * 5
235 = 5 * 47
270 = 2 * 3 * 3 * 3 * 5
The GCF is the product of the list of primes that appear in all of those numbers (125, 235, 270).
47 only appears as a factor in 235, so 47 does not appear in the GCF.
The only number that appears in all three numbers (125, 235, 270) is 5.
5 appears in 125 three times, but it only appears once in all three numbers (125, 235, 270), so the GCF only includes one 5.
Answer: The GCF of 125, 235, and 270 is 5.