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Yazan975

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In summary, To find the least common multiple of 12a^2bc, 8ab, and 4a^2cd, we can use the prime factorization method. The resulting least common multiple is 24a^2bcd. To find another term that would result in a least common multiple of 24a^3bc^2d, we need to add one more "a" and one more "c". Any coefficient must already be included in the "24". An odd prime number that divides 24 is 3.

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Yazan975

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MarkFL

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MHB

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Can you show what you've tried or your thoughts on how to begin?

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HOI

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Three of the terms are [tex]12a^2bc[/tex], [tex]8ab[/tex], and [tex]4a^2cd[/tex]. To find the least common multiple of those 3, note that [tex]12= 2^2(3)[/tex], [tex]8= 2^3[/tex], and [tex]4= 2^2[/tex]. The least common multiple of those three is [tex]2^3(3)= 24[/tex]. The highest power of a is [tex]a^2[/tex] and the highest power of b, c, and d is 1 for all three. So the least common multiple of those three terms is [tex]24a^2bcd[/tex]. We want another term such that the least common multiple of all four terms is [tex]24a^3bc^2d[/tex]. We already have the "24", the "b" and "d", two of the three "a"s, and one of the two "c"s. It looks like we need just one more "a" and one more "c". Any coefficient must be already included in the "24". What is an odd prime number that divides 24?

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A common multiple is a number that is a multiple of two or more other numbers. It is the smallest number that is divisible by all the given numbers.

To find the common multiple of two numbers, you can list out the multiples of each number and find the smallest number that appears in both lists. Another method is to use the prime factorization of the numbers and find the product of the highest powers of each prime factor.

Finding common multiples is important in simplifying fractions and solving problems involving fractions. It is also used in finding the lowest common denominator in adding or subtracting fractions.

The fourth term in a common multiple sequence refers to the fourth number in a list of numbers that are all multiples of a given number. For example, in the sequence 4, 8, 12, 16, the fourth term is 16.

Common multiple and least common multiple are closely related. The least common multiple is the smallest common multiple of two or more numbers, while a common multiple is any number that is divisible by all the given numbers. The least common multiple is also known as the lowest common multiple or smallest common denominator.

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