LCM of First 10 Natural Numbers

The least common multiple (LCM) of the first 10 natural numbers (1 through 10) is 2520.

To find the LCM, we first need to determine the prime factorization of each number:

• 1: 1
• 2: 2
• 3: 3
• 4: 2²
• 5: 5
• 6: 2 × 3
• 7: 7
• 8: 2³
• 9: 3²
• 10: 2 × 5

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

• Highest power of 2: 2³ (from 8)
• Highest power of 3: 3² (from 9)
• Highest power of 5: 5¹ (from 5 and 10)
• Highest power of 7: 7¹ (from 7)

Now, we calculate the LCM by multiplying these together:

LCM = 2³ × 3² × 5 × 7 = 8 × 9 × 5 × 7

Calculating this step by step:

• 8 × 9 = 72
• 72 × 5 = 360
• 360 × 7 = 2520

Thus, the LCM of the first 10 natural numbers is 2520.