Least Common Multiple

Definition

The least common multiple (LCM) is the smallest positive integer that is divisible by two or more given integers. It is a fundamental concept in mathematics that is closely related to finding factors and multiples of numbers, as well as understanding the relationships between fractions and decimals.

5 Must Know Facts For Your Next Test

1. The LCM of two or more numbers is the smallest positive integer that is divisible by all the given numbers.
2. To find the LCM, you can use the prime factorization method, where you find the prime factors of each number and then take the product of the highest power of each prime factor.
3. The LCM is often used to find a common denominator when adding or subtracting fractions with different denominators.
4. Understanding the LCM is crucial when working with fractions and decimals, as it helps you find the smallest common unit that can represent multiple numbers.
5. The LCM can also be used to find the least common denominator (LCD) when converting between fractions and decimals.

Review Questions

• Explain how the least common multiple (LCM) is used to find a common denominator when adding or subtracting fractions.
  • The LCM is used to find the least common denominator (LCD) when adding or subtracting fractions with different denominators. To do this, you first find the LCM of the denominators of the fractions. The LCM represents the smallest common unit that can represent all the fractions. Then, you convert each fraction to have the LCD as the denominator, which allows you to add or subtract the fractions with a common unit.
• Describe the relationship between the least common multiple (LCM) and prime factorization.
  • The LCM of two or more numbers is closely related to their prime factorization. To find the LCM, you need to find the prime factors of each number and then take the product of the highest power of each prime factor. This ensures that the LCM is the smallest positive integer that is divisible by all the given numbers. The prime factorization method is a key tool for determining the LCM, as it allows you to identify the unique prime factors that make up each number.
• Analyze how the understanding of the least common multiple (LCM) can help in the conversion between fractions and decimals.
  • Knowing the LCM is crucial when converting between fractions and decimals. The LCM can be used to find the least common denominator (LCD), which represents the smallest common unit that can express both the fraction and the decimal. By converting the fraction to have the LCD as the denominator, and the decimal to have the LCD as the denominator, you can establish a common basis for comparison and perform operations like addition, subtraction, and conversion between the two representations. The LCM is the key to ensuring that the fractions and decimals are expressed in a way that allows for accurate and meaningful comparisons.

Related terms

Factors:

Factors are the numbers that divide evenly into another number without a remainder.

Multiples:

Multiples are the products of a number and any integer.

Prime Factorization:

Prime factorization is the process of breaking a number down into its prime factors.