# Calculating LCD and GCD of 2 Sets of Numbers

• MHB
• karush
In summary, the greatest common divisor between (2^4 * 3^2 * 5 * 7^2) and (2 * 3^3 * 7 * 11) is 2 * 3^2 * 7 and the least common multiple is 2^3 * 3^3 * 5 * 7 * 11.
karush
Gold Member
MHB
Determine
$\textit{gcd}(2^4 \cdot 3^2 \cdot 5 \cdot 7^2,\quad 2 \cdot 3^3 \cdot 7 \cdot 11)$
and
$\textit{lcm}(2^3 \cdot 3^2 \cdot 5,\quad 2 \cdot 3^3 \cdot 7 \cdot 11)$

ok the example appeared to have combine the 2 sets on gcd but I am still ?

there is no book answer for this

Last edited:
Greatest Common divisor ... think about how you would factor out the common terms from both prime decompositions if they were added

$(2^4 \cdot 3^2 \cdot 5 \cdot 7^2) + (2 \cdot 3^3 \cdot 7 \cdot 11)$

${\color{red}(2 \cdot 3^2 \cdot 7)} \bigg[(2^3 \cdot 5 \cdot 7)+ ( 3 \cdot 11) \bigg]$Least Common Multiple ... think about obtaining a common denominator if both prime factor decompositions were denominators of two fractions

$\dfrac{x}{2^3 \cdot 3^2 \cdot 5} + \dfrac{y}{2 \cdot 3^3 \cdot 7 \cdot 11}$

$\dfrac{x(3 \cdot 7 \cdot 11) + y(2^2 \cdot 5)}{\color{red} 2^3 \cdot 3^3 \cdot 5 \cdot 7 \cdot 11}$

well that makes a lot more sense

i don't think there is any need to multiple these out

Last edited:

## 1. What is the difference between LCD and GCD?

The LCD (Least Common Denominator) is the smallest number that is divisible by all the denominators in a set of fractions. The GCD (Greatest Common Divisor) is the largest number that divides evenly into all the numbers in a set.

## 2. How do you calculate the LCD?

To calculate the LCD, you need to find the prime factorization of each denominator in the set. Then, multiply the highest power of each prime factor together to get the LCD.

## 3. How do you calculate the GCD?

To calculate the GCD, you need to find the prime factorization of each number in the set. Then, find the common prime factors and multiply them together to get the GCD.

## 4. What is the importance of calculating the LCD and GCD?

Calculating the LCD and GCD is important in simplifying fractions and solving equations involving fractions. It also helps in comparing and ordering fractions.

## 5. Can the LCD and GCD be calculated for more than 2 sets of numbers?

Yes, the LCD and GCD can be calculated for any number of sets of numbers. The process remains the same, finding the prime factorization and then finding the common prime factors.

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