Multiples are the products of a given number and any whole number. They represent the numbers in the multiplication table for that particular number, and are essential in understanding concepts like factors and divisibility.
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The multiples of a number are all the numbers that can be obtained by multiplying that number by any whole number.
Identifying the multiples of a number is an important step in finding the factors of that number.
Multiples can be used to determine if a number is divisible by another number, as a number is divisible by another if it is a multiple of that number.
The first few multiples of a number can be easily identified by looking at the multiplication table for that number.
Multiples are essential in understanding concepts like least common multiple (LCM) and greatest common factor (GCF).
Review Questions
Explain how multiples are related to factors and divisibility.
Multiples and factors are closely related concepts. The multiples of a number are the products of that number and any whole number, while the factors of a number are the numbers that divide evenly into that number. Identifying the multiples of a number is an important step in finding its factors, as a number is a factor of another number if the first number is a multiple of the second. Additionally, a number is divisible by another number if the first number is a multiple of the second.
Describe how the concept of multiples is used in finding the least common multiple (LCM) and greatest common factor (GCF) of two or more numbers.
The concept of multiples is essential in finding the least common multiple (LCM) and greatest common factor (GCF) of two or more numbers. The LCM is the smallest positive integer that is a multiple of all the given numbers, while the GCF is the largest positive integer that divides each of the given numbers without a remainder. To find the LCM, one can list the multiples of each number and identify the smallest number that appears in all the lists. To find the GCF, one can list the factors of each number and identify the largest number that appears in all the lists.
Analyze how the understanding of multiples can be used to solve problems related to divisibility and number patterns.
The understanding of multiples can be used to solve a variety of problems related to divisibility and number patterns. For example, knowing the multiples of a number can help determine if a number is divisible by another number, as a number is divisible by another if it is a multiple of that number. Additionally, the multiples of a number can be used to identify patterns in number sequences, such as the multiples of 3 (3, 6, 9, 12, etc.) or the multiples of 7 (7, 14, 21, 28, etc.). This knowledge can be applied to solve problems involving divisibility, factor trees, and the identification of number patterns.