Math Problem Statement

Find the lowest common multiple of 20 and 24

Solution

To find the lowest common multiple (LCM) of 20 and 24, we can follow these steps:

  1. Prime factorization:

    • 20=22×520 = 2^2 \times 5
    • 24=23×324 = 2^3 \times 3
  2. LCM is found by taking the highest powers of all prime factors that appear in both factorizations:

    • The highest power of 2 is 232^3.
    • The highest power of 3 is 313^1.
    • The highest power of 5 is 515^1.
  3. Multiply these together to get the LCM: LCM=23×31×51=8×3×5=120LCM = 2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 120

Therefore, the lowest common multiple of 20 and 24 is 120.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

  1. What is the greatest common divisor (GCD) of 20 and 24?
  2. How do you find the LCM of three numbers?
  3. Can you find the LCM of 24 and another number like 36?
  4. What is the relationship between LCM and GCD for two numbers?
  5. How can the LCM be used to solve problems involving fractions?

Tip: To quickly estimate the LCM, use the formula:
LCM(a,b)=a×bGCD(a,b)LCM(a, b) = \frac{a \times b}{GCD(a, b)}

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Math Problem Analysis

Mathematical Concepts

Number Theory
Prime Factorization
Least Common Multiple (LCM)

Formulas

LCM(a, b) = (a × b) / GCD(a, b)
Prime Factorization Method for LCM

Theorems

Fundamental Theorem of Arithmetic
LCM and GCD Relationship

Suitable Grade Level

Grades 6-8