Find the gcd and the lcm of the following 2 3rd 3 5th 5 7th

Find the gcd and the lcm of the following: 2 3rd 3 5th 5 7th 7 9th 11 and 2 9th 3 7th 5 5th 7 3rd 13

Solution

The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), or Highest Common Factor (HCF), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

In this example:

Factors of 23 are: 1 , 23.

Factors of 35 are: 1 , 5 , 7 , 35.

Factors of 57 are: 1 , 3 , 19 , 57.

Factors of 79 are: 1 , 79.

Factors of 11 are: 1 , 11.

We see that the Greatest Common Factor (Divisor) is 1.

Least Common Multiple (LCM) for 23 35 57 79 11 is 39874065.

Explanation

The Least Common Multiple (LCM) is the smallest number that two or more numbers will divide into evenly. NOTE: to find LCM you first need to know how to find GCD.

First we will find LCM for first two numbers ( 23 and 35 ).

Step 1: Find the GCD (Greatest Common Divisor ) of 23 and 35 which is 1.

Step 2: Multiply the numbers 23 and 35 together ( 23 * 35 = 805 )

Step 3: Divide the 805 with 1. (805/1 = 805)

So, the LCM of 23 and 35 is 805.

Now we will find the LCM of above result (805) and third number ( 57 ) using the same procedure.

The result of this part is 45885

Include all other numbers one by one.

and

Greatest Common Divisor (GCD) for 29 37 55 73 13 is 1.

Explanation

The Greatest Common Divisor (GCD), also known as the Greatest Common Factor (GCF), or Highest Common Factor (HCF), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.

In this example:

Factors of 29 are: 1 , 29.

Factors of 37 are: 1 , 37.

Factors of 55 are: 1 , 5 , 11 , 55.

Factors of 73 are: 1 , 73.

Factors of 13 are: 1 , 13.

We see that the Greatest Common Factor (Divisor) is 1.

Least Common Multiple (LCM) for 29 37 55 73 13 is 56005235.

Explanation

The Least Common Multiple (LCM) is the smallest number that two or more numbers will divide into evenly. NOTE: to find LCM you first need to know how to find GCD.

First we will find LCM for first two numbers ( 29 and 37 ).

Step 1: Find the GCD (Greatest Common Divisor ) of 29 and 37 which is 1.

Step 2: Multiply the numbers 29 and 37 together ( 29 * 37 = 1073 )

Step 3: Divide the 1073 with 1. (1073/1 = 1073)

So, the LCM of 29 and 37 is 1073.

Now we will find the LCM of above result (1073) and third number ( 55 ) using the same procedure.

The result of this part is 59015

Include all other numbers one by one.