Find the LCM of 2, 3, 4, 9, 5, 6, 7, 12

To find the Least Common Multiple (LCM) of the numbers 2, 3, 4, 9, 5, 6, 7, and 12, we can use the prime factorization method.

First, we identify the prime factorization of each number:

• 2 = 2
• 3 = 3
• 4 = 2²
• 9 = 3²
• 5 = 5
• 6 = 2 × 3
• 7 = 7
• 12 = 2² × 3

Next, we take the highest power of each prime number that appears in the factorizations:

• For prime number 2: Highest power is 2² (from 4 and 12)
• For prime number 3: Highest power is 3² (from 9)
• For prime number 5: Highest power is 5¹ (from 5)
• For prime number 7: Highest power is 7¹ (from 7)

Now we multiply these together to get the LCM:

LCM = 2² × 3² × 5¹ × 7¹ = 4 × 9 × 5 × 7

Calculating this step-by-step:

• 4 × 9 = 36
• 36 × 5 = 180
• 180 × 7 = 1260

Thus, the LCM of 2, 3, 4, 9, 5, 6, 7, and 12 is 1260.