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Location: Site Entrance < Arithmetic and Number Theory Skills << 10 LCM GCD and Euclid GCD Algorithm


10 LCM GCD and Euclid GCD Algorithm

     12 GCD 2700 288 via Primes
     1 Least Common Multiples LCM Introduction
     2 Least Common Multiple LCM intro via list method
     LCM 60 45 Avoid List Method Use Primes
     4 LCM of 8 and 10 via Primes
     5 Common Divisors 60 45 via Primes
     6 GCD from Primes
     7 GCD and LCM from prime factorization
     8 GCD from Euclidean Algorithm
     9 GCD of 360 110 via Primes and Euclid Algorithm
     10 Euclid Algorithm with 129 125 and with 45 14
     11 GCD 2700 288 via Euclid Algorithm
     13 GCD from given Prime Factorizations
     14 GCD of 650 110 via Primes LCM via Product Rule
     15 GCD of 650 225 via Euclid Alg LCM via Product Rule
     16 GCD and LCM of 650 225 via Primes
     17 GCD LCM of 85 and 60 via Primes

Notes

  1. Least Common Multiples [LCM] Introduction. This video lists the first 14 multiples of 6, and the first 6 multiples of 14 to see if there is a smaller common multiple that 6 × 14 = 14 × 6. The video provides a hint of the role of primes in find the LCM of the two numbers. ??? KILL

  2. Least Common Multiple LCM intro via list method. This video answers the question what is a LCM, explains the motivation for LCM calculation, and introduces the list method for finding the LCM of a pair of small whole numbers, here 6 and 8. For these two numbers, the list method begins by writing or listing the first 6 multiples of 8 and the first 8 multiples of 6 to be list

  3. LCM 60 45 Avoid List Method Use Primes. This video explains why the use of prime factorization requires less work than the list method to find the LCM for two numbers, namely 60 and 45. Includes a clear introduction of the prime factorization based method for finding LCMs.

  4. LCM of 8 and 10 via Primes. This video shows how to find the least common multiple of 8 and 10 using their prime factorizations. The video explains the method. The video includes the list method as well for confirmation.

  5. Common Divisors 60 45 via Primes. This video employs the prime factorizations of 60 and 45 - obtained in the previous lesson - may be used to generate common divisor and to identify the greatest common divisor.

    Optional Question: How many common divisors are their. Master section on Combinatorics to answer.

  6. GCDs from Primes. This video shows how prime factorization of whole numbers may be used to find the greatest common divisors of the whole numbers.

  7. GCD and LCM from prime factorization. This video gives examples of how to compute Greatest Common Divisor and Least Common Multiples of a pair of numbers, each equal to product of primes - their prime factorizations.

  8. GCD from Euclid's Algorithm. This video gives a first example of Euclid Algorithm for find the greatest common divisor of two numbers, here 875 and 300. It then simplifies the fraction 875 over 300. Finally, it shows how to construct a small - in fact the least - common multiple of them for use in addition of two fractions with denominators 875 nad 300.

  9. GCD of 360 110 via Primes and Euclidean Algorithm. This video calculates the GCD of 360 and 110 with Euclid Algorithm and then verifies the same result can be obtained from prime factorization. Euclid Algorithm may be quickest - proof of that or discovery of that is left to further studies in mathematics.

  10. Euclid Algorithm for 129 125 and for 45 14. This video provides two more examples of greatest common divisor calculation with Euclid's algorithm. The GCD in both examples is 1. Thus implies that in each pair of numbers, the pairs are relatively prime - their prime factorization share no common primes.

  11. GCD 2700 288 via Euclid's Algorithm. This video calculates the greatest common divisor of 2700 and 288 via Euclidean Algorithm. Then it employs the GCD to simplify a fraction where one is the numerator and the other is denominator. Lastly, it employs number obtained from the algorithm to obtain a Least Common Multiple - LCM

  12. GCD 2700 288 via Primes.This video calculates the greatest common divisor of 2700 and 288 using their prime factorizations

  13. GCD from given Prime Factorizations. This video shows how to calculate GCD for numbers given as products of primes. Three products are given. The products are consider in pairs. Question: What the GCD of all three numbers?

  14. GCD of 650 110 via Primes. Then LCM via Product Rule. The product of two numbers equals the product of their GCD and LCM. We call that relation, a product rule. If the product GCD × LCM is known along with one of the factors, then the other factor can be calculated. That represents a backward use of this product rule.

  15. GCD of 650 225 via Euclid Alg. Then LCM via Product Rule. This video calculates the GCD of the two numbers, and then uses the product rule introduced in the previous lesson to obtain the LCM. The next video confirms the GCD and LCM computed here by deriving them from prime factorizations.

  16. GCD and LCM of 650 225 via Primes. This video confirms the GCD and LCM computedin the previous video using prime factorizations.

  17. GCD LCM of 85 and 60 via Primes. This video calculates the GCD and LCM of the two numbers 85 and 60 with the aid of their prime factorizations.

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