2. Find out the LCM of the following
n
a.
6, 7, 9, 12, 14, 15, 18, 21,
24, 27, 28, 30, 33, 35
Answers
Answer:
LCM = 83,160
Step-by-step explanation:
List all prime factors for each number.
Prime Factorization of 6 is:
2 x 3 => 21 x 31
Prime Factorization of 7 shows:
7 is prime => 71
Prime Factorization of 9 is:
3 x 3 => 32
Prime Factorization of 12 is:
2 x 2 x 3 => 22 x 31
Prime Factorization of 14 is:
2 x 7 => 21 x 71
Prime Factorization of 15 is:
3 x 5 => 31 x 51
Prime Factorization of 18 is:
2 x 3 x 3 => 21 x 32
Prime Factorization of 21 is:
3 x 7 => 31 x 71
Prime Factorization of 24 is:
2 x 2 x 2 x 3 => 23 x 31
Prime Factorization of 27 is:
3 x 3 x 3 => 33
Prime Factorization of 28 is:
2 x 2 x 7 => 22 x 71
Prime Factorization of 30 is:
2 x 3 x 5 => 21 x 31 x 51
Prime Factorization of 33 is:
3 x 11 => 31 x 111
Prime Factorization of 35 is:
5 x 7 => 51 x 71
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, 3, 5, 7, 11
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 11 = 83160
In exponential form:
LCM = 23 x 33 x 51 x 71 x 111 = 83160
LCM = 83160
Therefore,
LCM(6, 7, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 33, 35) = 83,160