Calculate the value of the following expressions Show work g

Calculate the value of the following expressions. Show work!! gcd(432, 360) lcm(432, 360) gcd(4524, 5742) lcm(4524, 5742) gcd(59, 509). lcm(59, 509)

Solution

(a) Greatest Common Divisor (GCD) for 432 360 is 72.

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 432 are: 1 , 2 , 3 , 4 , 6 , 8 , 9 , 12 , 16 , 18 , 24 , 27 , 36 , 48 , 54 , 72 , 108 , 144 , 216 , 432.

Factors of 360 are: 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 12 , 15 , 18 , 20 , 24 , 30 , 36 , 40 , 45 , 60 , 72 , 90 , 120 , 180 , 360.

We see that the Greatest Common Factor (Divisor) is 72.

b)

Least Common Multiple (LCM) for 432 360 is 2160.

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.

Step 1: Find the GCD (Greatest Common Divisor ) of 432 and 360 which is 72.

Step 2: Multiply the numbers 432 and 360 together ( 432 * 360 = 155520 )

Step 3: Divide the 155520 with 72. (155520/72 = 2160)

So, the LCM of 432 and 360 is 2160.

(c)

Factors of 4524 are: 1 , 2 , 3 , 4 , 6 , 12 , 13 , 26 , 29 , 39 , 52 , 58 , 78 , 87 , 116 , 156 , 174 , 348 , 377 , 754 , 1131 , 1508 , 2262 , 4524.

Factors of 5742 are: 1 , 2 , 3 , 6 , 9 , 11 , 18 , 22 , 29 , 33 , 58 , 66 , 87 , 99 , 174 , 198 , 261 , 319 , 522 , 638 , 957 , 1914 , 2871 , 5742.

We see that the Greatest Common Factor (Divisor) is 174.

(d)

Least Common Multiple (LCM) for 4524 5742 is 149292.

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.

Step 1: Find the GCD (Greatest Common Divisor ) of 4524 and 5742 which is 174.

Step 2: Multiply the numbers 4524 and 5742 together ( 4524 * 5742 = 25976808 )

Step 3: Divide the 25976808 with 174. (25976808/174 = 149292)

So, the LCM of 4524 and 5742 is 149292.

(e)

Factors of 59 are: 1 , 59.

Factors of 509 are: 1 , 509.

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

Step 1: Find the GCD (Greatest Common Divisor ) of 59 and 509 which is 1.

Step 2: Multiply the numbers 59 and 509 together ( 59 * 509 = 30031 )

Step 3: Divide the 30031 with 1. (30031/1 = 30031)

So, the LCM of 59 and 509 is 30031.

hence the value is 30031