Math Problem Statement

Work out the lowest common multiple (LCM) of 8 and 10.

Solution

The task asks for the Lowest Common Multiple (LCM) of 8 and 10. Let's work through the solution step-by-step.

Steps to find the LCM of 8 and 10:

  1. Prime Factorization:

    • 8 = 2 × 2 × 2
    • 10 = 2 × 5
  2. Take the highest powers of all prime factors:

    • The primes involved are 2 and 5.
    • The highest power of 2 is 232^3 (from 8).
    • The highest power of 5 is 515^1 (from 10).
  3. Multiply these highest powers: LCM=23×51=8×5=40\text{LCM} = 2^3 \times 5^1 = 8 \times 5 = 40

Thus, the LCM of 8 and 10 is 40.

Do you need any further clarification, or have any other questions about LCM? Here are some related questions for you:

  1. How do we find the Greatest Common Divisor (GCD) of two numbers?
  2. What is the LCM of 12 and 15?
  3. How do we use prime factorization to calculate the LCM?
  4. How can LCM be used in real-life applications?
  5. Can the LCM be smaller than one of the numbers? Explain why or why not.

Tip: When calculating the LCM using prime factorization, always ensure to include every prime factor involved, using the highest exponent from both numbers.

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Math Problem Analysis

Mathematical Concepts

LCM
Prime Factorization

Formulas

LCM(a, b) = (a × b) / GCD(a, b)

Theorems

Fundamental Theorem of Arithmetic (Prime Factorization)

Suitable Grade Level

Grade 6-8