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Solved on Dec 09, 2023

Find the least common multiple (LCM) of $3, 8, 12$ .

STEP 1

Assumptions
1. We need to find the least common multiple (LCM) of the numbers 3, 8, and 12.
2. The LCM is the smallest number that is a multiple of all the given numbers.

STEP 2

First, we will list the prime factors of each number to find the LCM.
$3 = 3$ $8 = 2^3$ $12 = 2^2 \times 3$

STEP 3

Next, we identify the highest power of each prime number that appears in the factorization of the given numbers.
For prime number 2, the highest power is $2^3$ (from the number 8). For prime number 3, the highest power is $3^1$ (from the numbers 3 and 12).

STEP 4

Now, we will multiply these highest powers of prime numbers to find the LCM.
$LCM = 2^3 \times 3^1$

STEP 5

Calculate the LCM by multiplying the values.
$LCM = 8 \times 3$

STEP 6

Complete the multiplication to find the LCM.
$LCM = 24$
The least common multiple of 3, 8, and 12 is 24.

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