QuestionFind the least common denominator of $\frac{4}{35}, \frac{1}{77}, \frac{3}{22}$ . A. 110 B. 770 C. 2,695 D. 8,470 E. \$ 9,290

Studdy Solution

STEP 1

Assumptions1. The denominators of the fractions are35,77, and22. . We are looking for the least common denominator (LCD) which is the smallest number that is a multiple of all the denominators.

STEP 2

The least common denominator of the fractions can be found by finding the least common multiple (LCM) of the denominators. The LCM of numbers is the smallest number that is a multiple of all the numbers.
$LCD = LCM(35,77,22)$

STEP 3

To find the LCM of the numbers, we first find the prime factorization of each number.
Prime factorization of35 is $5 \times7$ . Prime factorization of77 is $7 \times11$ . Prime factorization of22 is $2 \times11$ .

STEP 4

The LCM of the numbers is found by multiplying each prime factor the greatest number of times it occurs in either number.
$LCM(35,77,22) =2^1 \times^1 \times7^1 \times11^1$

STEP 5

Calculate the LCM.
$LCM(35,77,22) =2 \times5 \times7 \times11 =770$ The least common denominator of the fractions $\frac{4}{35}, \frac{1}{77}$ , and $\frac{3}{22}$ is770.

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QuestionFind the least common denominator of $\frac{4}{35}, \frac{1}{77}, \frac{3}{22}$ . A. 110 B. 770 C. 2,695 D. 8,470 E. \$ 9,290

Studdy Solution

STEP 1

Assumptions1. The denominators of the fractions are35,77, and22. . We are looking for the least common denominator (LCD) which is the smallest number that is a multiple of all the denominators.

STEP 2

The least common denominator of the fractions can be found by finding the least common multiple (LCM) of the denominators. The LCM of numbers is the smallest number that is a multiple of all the numbers.
$LCD = LCM(35,77,22)$

STEP 3

To find the LCM of the numbers, we first find the prime factorization of each number.
Prime factorization of35 is $5 \times7$ . Prime factorization of77 is $7 \times11$ . Prime factorization of22 is $2 \times11$ .

STEP 4

The LCM of the numbers is found by multiplying each prime factor the greatest number of times it occurs in either number.
$LCM(35,77,22) =2^1 \times^1 \times7^1 \times11^1$

STEP 5

Calculate the LCM.
$LCM(35,77,22) =2 \times5 \times7 \times11 =770$ The least common denominator of the fractions $\frac{4}{35}, \frac{1}{77}$ , and $\frac{3}{22}$ is770.

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QuestionFind the least common denominator of 435,177,322\frac{4}{35}, \frac{1}{77}, \frac{3}{22}354​,771​,223​. A. 110 B. 770 C. 2,695 D. 8,470 E. \$ 9,290

Studdy Solution

STEP 1

Assumptions1. The denominators of the fractions are35,77, and22. . We are looking for the least common denominator (LCD) which is the smallest number that is a multiple of all the denominators.

STEP 2

The least common denominator of the fractions can be found by finding the least common multiple (LCM) of the denominators. The LCM of numbers is the smallest number that is a multiple of all the numbers.LCD=LCM(35,77,22)LCD = LCM(35,77,22)LCD=LCM(35,77,22)

STEP 3

To find the LCM of the numbers, we first find the prime factorization of each number.Prime factorization of35 is 5×75 \times75×7. Prime factorization of77 is 7×117 \times117×11. Prime factorization of22 is 2×112 \times112×11.

STEP 4

The LCM of the numbers is found by multiplying each prime factor the greatest number of times it occurs in either number.LCM(35,77,22)=21×1×71×111LCM(35,77,22) =2^1 \times^1 \times7^1 \times11^1LCM(35,77,22)=21×1×71×111

STEP 5

Calculate the LCM.LCM(35,77,22)=2×5×7×11=770LCM(35,77,22) =2 \times5 \times7 \times11 =770LCM(35,77,22)=2×5×7×11=770The least common denominator of the fractions 435,177\frac{4}{35}, \frac{1}{77}354​,771​, and 322\frac{3}{22}223​ is770.

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QuestionFind the least common denominator of $\frac{4}{35}, \frac{1}{77}, \frac{3}{22}$ . A. 110 B. 770 C. 2,695 D. 8,470 E. \$ 9,290

The least common denominator of the fractions can be found by finding the least common multiple (LCM) of the denominators. The LCM of numbers is the smallest number that is a multiple of all the numbers.
$LCD = LCM(35,77,22)$

To find the LCM of the numbers, we first find the prime factorization of each number.
Prime factorization of35 is $5 \times7$ . Prime factorization of77 is $7 \times11$ . Prime factorization of22 is $2 \times11$ .

The LCM of the numbers is found by multiplying each prime factor the greatest number of times it occurs in either number.
$LCM(35,77,22) =2^1 \times^1 \times7^1 \times11^1$

Calculate the LCM.
$LCM(35,77,22) =2 \times5 \times7 \times11 =770$ The least common denominator of the fractions $\frac{4}{35}, \frac{1}{77}$ , and $\frac{3}{22}$ is770.