What is the least number divisible by all the numbers from 1 to 8?

The least number divisible by all the numbers from 1 to 8 is 840.

Finding the Least Common Multiple (LCM)

According to the reference, the least number divisible by all the numbers from 1 to 8 is the Least Common Multiple (LCM) of these numbers. Finding the LCM requires identifying the prime factors of each number and then multiplying the highest power of each prime factor together.

Here's a breakdown:

• Numbers: 1, 2, 3, 4, 5, 6, 7, 8
• Prime Factorization:
  • 1: 1
  • 2: 2
  • 3: 3
  • 4: 2²
  • 5: 5
  • 6: 2 x 3
  • 7: 7
  • 8: 2³

Calculating the LCM

To find the LCM, we take the highest power of each prime factor present in the numbers:

• 2³ (from 8)
• 3¹ (from 3 or 6)
• 5¹ (from 5)
• 7¹ (from 7)

Multiplying these together:

LCM = 2³ 3 5 7 = 8 3 5 7 = 24 * 35 = 840

Practical Insights

• Understanding LCM is essential in various mathematical applications, such as solving problems related to time, distance, and fractions.
• The LCM of a set of numbers is the smallest number that each of those numbers divides into without leaving a remainder.

Therefore, 840 is the smallest number that can be divided by each number from 1 to 8 without leaving a remainder.