QuestionFind the least common multiple (LCM) of 84 and 56.

Studdy Solution

STEP 1

Assumptions1. We need to find the least common multiple (LCM) of84 and56. . The LCM of two numbers is the smallest positive integer that is divisible by both numbers.

STEP 2

The first step to find the LCM of two numbers is to find the prime factorization of each number. Let's start with84.

STEP 3

To find the prime factorization of84, we start by dividing it by the smallest prime number, which is2.
$84 /2 =42$

STEP 4

We continue dividing by2 until we can't anymore.
$42 /2 =21$

STEP 5

Now, we can't divide by2 anymore, so we move to the next prime number, which is3.
$21 /3 =7$

STEP 6

Finally, we divide by, which is also a prime number.
$/ =1$

STEP 7

So, the prime factorization of84 is $2^2 3 7$ .

STEP 8

Now, let's find the prime factorization of56. We start by dividing it by the smallest prime number, which is2.
$56 /2 =28$

STEP 9

We continue dividing by2 until we can't anymore.
$28 /2 =14$ $14 /2 =7$

STEP 10

Finally, we divide by7, which is also a prime number.
$7 /7 =$

STEP 11

So, the prime factorization of56 is $^3 *7$ .

STEP 12

To find the LCM of84 and56, we take the highest power of each prime number from the prime factorizations of84 and56.

STEP 13

The highest power of2 is $2^3$ , the highest power of3 is $3$ , and the highest power of7 is $7$ .

STEP 14

So, the LCM of84 and56 is $2^3 3 7$ .

STEP 15

Calculate the LCM.
$LCM =2^3 3 7 =8 3 7 =168$ The least common multiple of84 and56 is168.

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QuestionFind the least common multiple (LCM) of 84 and 56.

Studdy Solution

STEP 1

Assumptions1. We need to find the least common multiple (LCM) of84 and56. . The LCM of two numbers is the smallest positive integer that is divisible by both numbers.

STEP 2

The first step to find the LCM of two numbers is to find the prime factorization of each number. Let's start with84.

STEP 3

To find the prime factorization of84, we start by dividing it by the smallest prime number, which is2.
$84 /2 =42$

STEP 4

We continue dividing by2 until we can't anymore.
$42 /2 =21$

STEP 5

Now, we can't divide by2 anymore, so we move to the next prime number, which is3.
$21 /3 =7$

STEP 6

Finally, we divide by, which is also a prime number.
$/ =1$

STEP 7

So, the prime factorization of84 is $2^2 3 7$ .

STEP 8

Now, let's find the prime factorization of56. We start by dividing it by the smallest prime number, which is2.
$56 /2 =28$

STEP 9

We continue dividing by2 until we can't anymore.
$28 /2 =14$ $14 /2 =7$

STEP 10

Finally, we divide by7, which is also a prime number.
$7 /7 =$

STEP 11

So, the prime factorization of56 is $^3 *7$ .

STEP 12

To find the LCM of84 and56, we take the highest power of each prime number from the prime factorizations of84 and56.

STEP 13

The highest power of2 is $2^3$ , the highest power of3 is $3$ , and the highest power of7 is $7$ .

STEP 14

So, the LCM of84 and56 is $2^3 3 7$ .

STEP 15

Calculate the LCM.
$LCM =2^3 3 7 =8 3 7 =168$ The least common multiple of84 and56 is168.

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QuestionFind the least common multiple (LCM) of 84 and 56.

Studdy Solution

STEP 1

Assumptions1. We need to find the least common multiple (LCM) of84 and56. . The LCM of two numbers is the smallest positive integer that is divisible by both numbers.

STEP 2

The first step to find the LCM of two numbers is to find the prime factorization of each number. Let's start with84.

STEP 3

To find the prime factorization of84, we start by dividing it by the smallest prime number, which is2.84/2=4284 /2 =4284/2=42

STEP 4

We continue dividing by2 until we can't anymore.42/2=2142 /2 =2142/2=21

STEP 5

Now, we can't divide by2 anymore, so we move to the next prime number, which is3.21/3=721 /3 =721/3=7

STEP 6

Finally, we divide by, which is also a prime number./=1 / =1/=1

STEP 7

So, the prime factorization of84 is 22∗3∗72^2 *3 *722∗3∗7.

STEP 8

Now, let's find the prime factorization of56. We start by dividing it by the smallest prime number, which is2.56/2=2856 /2 =2856/2=28

STEP 9

We continue dividing by2 until we can't anymore.28/2=1428 /2 =1428/2=1414/2=714 /2 =714/2=7

STEP 10

Finally, we divide by7, which is also a prime number.7/7=7 /7 =7/7=

STEP 11

So, the prime factorization of56 is 3∗7^3 *73∗7.

STEP 12

To find the LCM of84 and56, we take the highest power of each prime number from the prime factorizations of84 and56.

STEP 13

The highest power of2 is 232^323, the highest power of3 is 333, and the highest power of7 is 777.

STEP 14

So, the LCM of84 and56 is 23∗3∗72^3 *3 *723∗3∗7.

STEP 15

Calculate the LCM.LCM=23∗3∗7=8∗3∗7=168LCM =2^3 *3 *7 =8 *3 *7 =168LCM=23∗3∗7=8∗3∗7=168The least common multiple of84 and56 is168.

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To find the prime factorization of84, we start by dividing it by the smallest prime number, which is2.
$84 /2 =42$

We continue dividing by2 until we can't anymore.
$42 /2 =21$

Now, we can't divide by2 anymore, so we move to the next prime number, which is3.
$21 /3 =7$

Finally, we divide by, which is also a prime number.
$/ =1$

So, the prime factorization of84 is $2^2 3 7$ .

Now, let's find the prime factorization of56. We start by dividing it by the smallest prime number, which is2.
$56 /2 =28$

We continue dividing by2 until we can't anymore.
$28 /2 =14$ $14 /2 =7$

Finally, we divide by7, which is also a prime number.
$7 /7 =$

So, the prime factorization of56 is $^3 *7$ .

The highest power of2 is $2^3$ , the highest power of3 is $3$ , and the highest power of7 is $7$ .

So, the LCM of84 and56 is $2^3 3 7$ .

Calculate the LCM.
$LCM =2^3 3 7 =8 3 7 =168$ The least common multiple of84 and56 is168.