What is the GCD and LCM of 35280 and 4158?

  • MHB
  • Thread starter karush
  • Start date
In summary, the greatest common divisor of $2^4 \cdot 3^2 \cdot 5 \cdot 7^2$ and $2 \cdot 3^3 \cdot 7 \cdot 11$ is $126$ and the least common multiple is $1164240$. The number displayed by Wolfram Alpha is $83160$, which is the incorrect value for the least common multiple. The correct term is "least common multiple", not "least common divisor".
  • #1
karush
Gold Member
MHB
3,269
5
Determine
$gcd(2^4 \cdot 3^2 \cdot 5 \cdot 7^2, 2 \cdot 3^3 \cdot 7 \cdot 11)=\boxed{126}$
and
$lcd(2^3 \cdot 3^2 \cdot 5,2 \cdot 3^3 \cdot 7 \cdot 11)=\boxed{83160}$
the number in the box is what W$\vert$A returned
ok i was doing stuff like this about a year ago but forgot
so assume to start
$gcd(35280,4158)$
but can't we take advantage of the powers
 
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  • #2
prime factorization …

$35280 = 2^4 \cdot 3^2 \cdot 5 \cdot 7^2$
$4158 = 2 \cdot 3^3 \cdot 7 \cdot 11$

greatest common divisor includes the least power of all common factors …
$2 \cdot 3^2 \cdot 7 = 126$

least common multiple includes the greatest power of all common factors and the factors the two values do not have in common …
$2^4 \cdot 3^3 \cdot 5 \cdot 7^2 \cdot 11 = 1164240$
 
  • #3
Mahalo
so its just choosing the powers then calculate
 
  • #4
karush said:
Mahalo
so its just choosing the powers then calculate
Well, it is knowing what these things are, what their definitions are!

And note that it is "least common multiple", "lcm", NOT "lcd".
 
  • #5
corrected
 

Related to What is the GCD and LCM of 35280 and 4158?

1. What is the meaning of GCD and LCM?

The GCD (Greatest Common Divisor) and LCM (Least Common Multiple) are mathematical concepts used to find the largest common factor and smallest common multiple of two or more numbers, respectively.

2. How do you calculate the GCD and LCM?

To calculate the GCD of two numbers, you can use the Euclidean algorithm, which involves finding the remainder of dividing the larger number by the smaller number and repeating the process until the remainder is 0. The last non-zero remainder is the GCD. To calculate the LCM, you can use the formula LCM = (a * b) / GCD(a, b), where a and b are the two numbers.

3. What is the GCD and LCM of 35280 and 4158?

The GCD of 35280 and 4158 is 18, and the LCM is 1,034,680.

4. Why is finding the GCD and LCM important?

Knowing the GCD and LCM can be useful in simplifying fractions, finding equivalent fractions, and solving problems involving ratios and proportions.

5. Can the GCD and LCM be used for more than two numbers?

Yes, the GCD and LCM can be calculated for any number of numbers. To find the GCD, you can use the same process as with two numbers, finding the GCD of the GCD and the next number. To find the LCM, you can use the formula LCM = (a * b * c * ...) / GCD(a, b, c, ...), where a, b, c, etc. are the numbers.

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