find the LCM of the following numbers by prime factorization method 180,192,576 with solution plz explain
Answers
Answer:
2880
Step-by-step explanation:
List all prime factors for each number.
Prime Factorization of 180 is:
2 x 2 x 3 x 3 x 5 => 22 x 32 x 51
Prime Factorization of 192 is:
2 x 2 x 2 x 2 x 2 x 2 x 3 => 26 x 31
Prime Factorization of 576 is:
2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 => 26 x 32
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 2, 2, 2, 3, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5 = 2880
In exponential form:
LCM = 26 x 32 x 51 = 2880
LCM = 2880
Therefore,
LCM(180, 192, 576) = 2880
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Answer:
the lcm of 180,192,576 is 2880
Step-by-step explanation:
2/180,192,576
2/90,96,288
2/45,48,144
2/45,24,72
2/45,12,36
3/45,3,9
3/15,1,3
3/5,1,1
the multiplication of 2x2x2x2x2x3x3x3x = 2880