What is the lcm for 10 and 8

General
1

what is the lcm for 10 and 8

2

What is the LCM for 10 and 8?

Answer:
The Least Common Multiple (LCM) of two numbers is the smallest positive integer that is divisible by both numbers. To find the LCM of 10 and 8, follow these steps:

Step-by-Step Method to Find LCM:

1. Prime Factorization:

  • First, determine the prime factors of each number.
  • Prime factorization of 10:
    10 = 2 \times 5
  • Prime factorization of 8:
    8 = 2^3

2. Identify the Highest Powers of All Prime Factors:

  • List all the prime factors with their highest powers that appear in the factorizations.
  • For 10, the prime factors are (2) and (5).
  • For 8, the prime factor is (2).
  • The highest power of (2) is (2^3) (from 8).
  • The highest power of (5) is (5) (from 10).

3. Calculate the LCM:

  • Multiply the highest powers of all prime factors to find the LCM.
    \text{LCM} = 2^3 \times 5
  • Compute the value:
    2^3 = 8
    8 \times 5 = 40

Conclusion:

Therefore, the Least Common Multiple (LCM) of 10 and 8 is ( \boxed{40} ).