find the LCM of the following numbers by the prime factorization method a 144, 180 b. 106, 159 , 371
Answers
Step-by-step explanation:
a.
List all prime factors for each number.
Prime Factorization of 144 is:
2 x 2 x 2 x 2 x 3 x 3 => 24 x 32
Prime Factorization of 180 is:
2 x 2 x 3 x 3 x 5 => 22 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, 2, 3, 3, 5
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720
In exponential form:
LCM = 24 x 32 x 51 = 720
LCM = 720
Therefore,
LCM(144, 180) = 720
b.
List all prime factors for each number.
Prime Factorization of 106 is:
2 x 53 => 21 x 531
Prime Factorization of 159 is:
3 x 53 => 31 x 531
Prime Factorization of 371 is:
7 x 53 => 71 x 531
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, 3, 7, 53
Multiply these factors together to find the LCM.
LCM = 2 x 3 x 7 x 53 = 2226
In exponential form:
LCM = 21 x 31 x 71 x 531 = 2226
LCM = 2226
Therefore,
LCM(106, 159, 371) = 2226
Answer:
a.720 b.53
Step-by-step explanation:
prime factorization of 144, 180 Is 2×2×2×2×3×3×5