Math Problem Statement

What is the least common multiple of 5 and 18?

Solution

The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both. To find the LCM of 5 and 18:

  1. Prime factorize each number:

    • 5 is already a prime number: 5=515 = 5^1
    • 18 can be factored into primes: 18=21×3218 = 2^1 \times 3^2
  2. For the LCM, take the highest power of each prime factor that appears:

    • The prime factors are 2, 3, and 5.
    • From 18, we take 212^1 and 323^2.
    • From 5, we take 515^1.
  3. Multiply these together: LCM=21×32×51=2×9×5=90LCM = 2^1 \times 3^2 \times 5^1 = 2 \times 9 \times 5 = 90

So, the least common multiple of 5 and 18 is 90.

Would you like more details or have any other questions?

Here are 5 related questions to explore:

  1. What is the LCM of 12 and 15?
  2. How does the LCM relate to the greatest common divisor (GCD)?
  3. Can you explain the method to find the LCM using division?
  4. What are the applications of the LCM in solving real-world problems?
  5. How would you find the LCM of three numbers?

Tip: LCM is particularly useful for adding or subtracting fractions where the denominators differ.

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Math Problem Analysis

Mathematical Concepts

Number Theory
Least Common Multiple (LCM)
Prime Factorization

Formulas

LCM formula using prime factorization
LCM(a, b) = (a × b) / GCD(a, b)

Theorems

Fundamental Theorem of Arithmetic

Suitable Grade Level

Grades 5-7