Multiple

Definition

A multiple is a number that can be expressed as the product of an integer and another integer. This concept is foundational in understanding divisibility, as a number is considered a multiple of another if it can be divided by that number without leaving a remainder. Additionally, multiples are crucial in calculating the least common multiple, which identifies the smallest multiple shared by two or more numbers, facilitating problem-solving in various mathematical contexts.

5 Must Know Facts For Your Next Test

1. The first multiple of any integer is the integer itself.
2. Multiples are generated by multiplying an integer by whole numbers (0, 1, 2, 3, ...).
3. Every integer has infinitely many multiples, which means there is no upper limit to how many multiples can be found.
4. Multiples of a number are always evenly spaced on the number line, with the distance between each multiple being equal to that number.
5. Finding the least common multiple of two numbers often involves listing their multiples and identifying the smallest one they have in common.

Review Questions

• How do you determine if one number is a multiple of another?
  • To determine if one number is a multiple of another, divide the first number by the second. If the division results in an integer with no remainder, then the first number is indeed a multiple of the second. This relationship highlights how multiples relate directly to the concept of divisibility and can help solve problems involving ratios and proportions.
• What process would you use to find the least common multiple of two given numbers?
  • To find the least common multiple (LCM) of two numbers, start by listing out their multiples until you identify the smallest number that appears in both lists. Alternatively, you can use prime factorization to express both numbers as products of prime factors and then multiply each factor at its highest exponent. This method effectively shows how multiples interact and converge at their least common multiple.
• Evaluate how understanding multiples impacts problem-solving in real-life situations, such as scheduling events.
  • Understanding multiples plays a crucial role in real-life scenarios like scheduling events or planning resources. For example, when trying to coordinate activities that occur at different intervals, knowing the least common multiple helps identify when those events will align. This not only streamlines planning but also enhances efficiency by ensuring that overlapping resources are optimally used. Hence, grasping the concept of multiples can significantly simplify complex logistical challenges.

Related terms

divisor: A divisor is a number that divides another number without leaving a remainder.

greatest common divisor (GCD): The greatest common divisor is the largest number that divides two or more integers without leaving a remainder.

prime number: A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.