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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
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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
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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
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GCD 2700 288 via Primes.This video calculates the greatest
common divisor of 2700 and 288 using their prime factorizations
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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?
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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.
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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.
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GCD and LCM of 650 225 via Primes. This video confirms the GCD and LCM
computedin the previous video using prime factorizations.
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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.