Find the greatest number with which 72,180and360 are exactly divisible
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Answer:-
LCM = 360
Solution by Prime Factorization
List all prime factors for each number.
Prime Factorization of 72 is:
2 x 2 x 2 x 3 x 3 => 23 x 32
Prime Factorization of 180 is:
2 x 2 x 3 x 3 x 5 => 22 x 32 x 51
Prime Factorization of 360 is:
2 x 2 x 2 x 3 x 3 x 5 => 23 x 32 x 51
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, 3, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 3 x 5 = 360
In exponential form:
LCM = 23 x 32 x 51 = 360
LCM = 360
Therefore,
LCM(72, 180, 360) = 360
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