Respuesta :
we know that
The LCD is the LCM (least common multiple) of all the denominators.
we have
[tex] 1/3, 3/4, 5/32, 8/9 [/tex]
[tex] 3=3^{1} \\ 4=2^{2} \\ 32=2^{5} \\ 9=3^{2} [/tex]
[tex] LCM=2^{5} *3^{2} \\ LCM=32*9\\ LCM=288 [/tex]
So
The LCM of [tex] 3, 4, 32, 9 [/tex] is [tex] 288 [/tex] ,
which is the multiple of the highest power of prime factors from all of the given numbers
therefore
the answer is
[tex] 288 [/tex]
The LCD for the fractions [tex]\dfrac{1}{3}[/tex], [tex]\dfrac{3}{4}[/tex], [tex]\dfrac{5}{32}[/tex] and [tex]\dfrac{8}{9}[/tex] is [tex]\boxed{288}[/tex].
Further explanation:
The LCD (least common denominator) is least common multiples of denominators.
The least common multiple is defined as the smallest number that divides all the given numbers.
Prime factorization is defined as the factors of the given number are only prime number.
Prime number is defined as a numbers that has only two factors one and itself.
Given:
The given numbers are [tex]\dfrac{1}{3}[/tex], [tex]\dfrac{3}{4}[/tex], [tex]\dfrac{5}{32}[/tex] and [tex]\dfrac{8}{9}[/tex].
Explanation:
First we have to find the prime factors of the denominators of all the numbers.
The prime factors of [tex]3[/tex] can be expressed as,
[tex]3 = {3^1}[/tex]
The prime factors of [tex]4[/tex] can be expressed as,
[tex]4 = {2^2}[/tex]
The prime factors of [tex]32[/tex] can be expressed as,
[tex]32 = {2^5}[/tex]
The prime factors of [tex]9[/tex] can be expressed as,
[tex]9 = {3^2}[/tex]
The least common factors are [tex]{2^5}[/tex] and [tex]{3^2}[/tex].
The least common denominator can be calculated as,
[tex]\begin{aligned}\text{LCD} &= {2^5} \times {3^2} \\ &= 32 \times 9\\&= 288\\ \end{aligned}[/tex]
The LCD for the fractions [tex]\dfrac{1}{3}[/tex], [tex]\dfrac{3}{4}[/tex], [tex]\dfrac{5}{32}[/tex] and [tex]\dfrac{8}{9}[/tex] is [tex]\boxed{288}[/tex].
Learn more:
1. Learn more about addition of two numbers https://brainly.com/question/894273
2. Learn more about multiplication https://brainly.com/question/4892332
Answer details:
Grade: Junior School
Subject: Mathematics
Chapter: Number system
Keywords: prime numbers, Least common denominator, LCD, Least common multiple, LCM, divide, prime factors, factorization, Prime factorization, factors, fraction, [tex]\dfrac{1}{3}[/tex], [tex]\dfrac{3}{4}[/tex], [tex]\dfrac{5}{32}[/tex], [tex]\dfrac{8}{9}[/tex].
