Math Problem Statement

Find the Least Common Multiple (LCM) of 10 and 18.

Solution

From the image, you are looking for the Least Common Multiple (LCM) of the numbers 10 and 18.

Steps to find the LCM:

  1. Prime factorization:

    • 10=2×510 = 2 \times 5
    • 18=2×3218 = 2 \times 3^2
  2. Take the highest powers of all prime factors:

    • From 1010: 21,512^1, 5^1
    • From 1818: 21,322^1, 3^2
    • Highest powers: 21,32,512^1, 3^2, 5^1
  3. Multiply the highest powers: LCM=21×32×51=2×9×5=90LCM = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90

Final Answer:

The LCM of 10 and 18 is 90.


Would you like further clarification or another example? 😊

Related Questions:

  1. What is the greatest common divisor (GCD) of 10 and 18?
  2. Can you find the LCM of three numbers (e.g., 10, 18, and 12)?
  3. How is the relationship between LCM and GCD expressed mathematically?
  4. Why is finding the LCM important in solving fraction problems?
  5. What are some real-life applications of the LCM concept?

Tip:

For quick LCM calculations, use the formula: LCM(a,b)=a×bGCD(a,b)LCM(a, b) = \frac{a \times b}{\text{GCD}(a, b)}

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Math Problem Analysis

Mathematical Concepts

Number Theory
Least Common Multiple (LCM)
Prime Factorization

Formulas

LCM(a, b) = (a × b) / GCD(a, b)
Prime factorization to find LCM

Theorems

Fundamental Theorem of Arithmetic

Suitable Grade Level

Grades 5-7