Answer:

LCM=12

Step-by-step explanation:

✏️Listing multiplies:

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✏️Find and list multiples of each number until the first common multiple is found. This is the lowest common multiple.

Multiples of 2:

2, 4, 6, 8, 10, 12, 14, 16

Multiples of 3:

3, 6, 9, 12, 15, 18

Multiples of 4:

4, 8, 12, 16, 20

Therefore,

LCM(2, 3, 4) = 12

✏️Prime Factorization:

✏️List all prime factors for each number.

Prime Factorization of 2 shows:

2 is prime => 21

Prime Factorization of 3 shows:

3 is prime => 31

Prime Factorization of 4 is:

2 x 2 => 22

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, 3

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 = 12

In exponential form:

LCM = 22 x 31 = 12

LCM = 12

Therefore,

LCM(2, 3, 4) = 12

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✏️GCF Method:

LCM(2, 3, 4) =

LCM(LCM(2, 3), 4)

Working from the innermost parentheses outward:

LCM(2,3) = (2 × 3) / GCF(2,3)

= (2 × 3) / 1

= 6 / 1

= 6

LCM(6,4) = (6 × 4) / GCF(6,4)

= (6 × 4) / 2

= 24 / 2

= 12

Therefore,

LCM(2, 3, 4) = 12