How to Find the GCD and LCD in Mathematics?

  • MHB
  • Thread starter karush
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In summary, the conversation discusses the differences and significance of GCD and LCD, how to find the GCD of two numbers using the Euclidean Algorithm, and the relationship between GCD and LCM. GCD is the largest number that divides evenly into two or more numbers, while LCD is the smallest number that is a multiple of two or more numbers. Finding the GCD and LCD is important in mathematics and computer science, and they are always positive numbers. GCD and LCM are different concepts, with GCD focusing on division and LCM focusing on multiplication.
  • #1
karush
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MHB
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$$\tiny{g1.1.2 \qquad UHW412}$$
\begin{align*}\displaystyle
S&=gcd(2^4\cdot3^2\cdot 5\cdot 7^2,2\cdot3^3\cdot 7\cdot 11)\\
&=gcd(35280,4158)\\
W|A&=126\\
\end{align*}

ok I tried to find a direct example but the powers and bases are mixed
the answer came from W|A

just interested in what steps are the normal protocol for this
 
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  • #2
I would look at all factors present, and take the smaller power present in each:

\(\displaystyle 2\cdot3^2\cdot7=126\)
 
  • #3
what about 5 and 11
 
  • #4
karush said:
what about 5 and 11
Only use the primes that are in both. So we ignore the 5 and 11.

-Dan
 

FAQ: How to Find the GCD and LCD in Mathematics?

1.

What is the difference between GCD and LCD?

GCD (Greatest Common Divisor) is the largest positive number that divides evenly into two or more numbers. LCD (Least Common Denominator) is the smallest number that is a multiple of two or more numbers. While GCD is used to simplify fractions, LCD is used to find a common denominator for fractions.

2.

How do you find the GCD of two numbers?

To find the GCD of two numbers, you can use the Euclidean Algorithm. This involves dividing the larger number by the smaller number and using the remainder as the new divisor. Continue this process until the remainder is 0. The last non-zero remainder is the GCD of the two numbers.

3.

What is the significance of finding the GCD and LCD?

Finding the GCD and LCD is important in many areas of mathematics, including simplifying fractions, finding equivalent fractions, and solving equations involving fractions. It is also used in programming and computer science to optimize algorithms and reduce the complexity of operations.

4.

Can the GCD or LCD be negative?

No, the GCD and LCD are always positive numbers. This is because they represent the largest or smallest possible value that can be divided evenly into two or more numbers. In some cases, the GCD or LCD may be 0, indicating that the numbers have no common factors or can't be reduced any further.

5.

What is the difference between GCD and LCM?

GCD (Greatest Common Divisor) and LCM (Least Common Multiple) are two different concepts. While GCD is used to find the largest number that divides evenly into two or more numbers, LCM is used to find the smallest positive number that is a multiple of two or more numbers. In other words, GCD focuses on division while LCM focuses on multiplication.

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