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- https://math.libretexts.org/Courses/Santiago_Canyon_College/HiSet_Mathematica_(Lopez)/06%3A_Exponentes_raices_y_factorizacion_de_numeros_enteros/6.05%3A_El_multiplo_menos_comun\(\begin{array} {ccll} {90} & = & {2 \cdot 45 = 2 \cdot 3 \cdot 15 = 2 \cdot 3 \cdot 3 \cdot 5 = 2 \cdot 3^2 \cdot 5} & {} \\ {630} & = & {2 \cdot 315 = 2 \cdot 3 \cdot 105 = 2 \cdot 3 \cdot 3 \cdot 3...\(\begin{array} {ccll} {90} & = & {2 \cdot 45 = 2 \cdot 3 \cdot 15 = 2 \cdot 3 \cdot 3 \cdot 5 = 2 \cdot 3^2 \cdot 5} & {} \\ {630} & = & {2 \cdot 315 = 2 \cdot 3 \cdot 105 = 2 \cdot 3 \cdot 3 \cdot 35} & {= 2 \cdot 3 \cdot 3 \cdot 5 \cdot 7} \\ {} & \ & {} & {= 2 \cdot 3^2 \cdot 5 \cdot 7} \end{array}\)
- https://math.libretexts.org/Courses/College_of_the_Canyons/Math_130%3A_Math_for_Elementary_School_Teachers_(Lagusker)/05%3A_Number_Theory/5.05%3A_The_Least_Common_MultipleThe LCM is the smallest number that is a multiple of all numbers, excluding zero. To find the LCM, we work backwards, following the three steps below. If you want to have the same number of each type ...The LCM is the smallest number that is a multiple of all numbers, excluding zero. To find the LCM, we work backwards, following the three steps below. If you want to have the same number of each type of cookie, what is the least number of each that you will need to make using complete recipes? Add (and Subtract) Fractions Using the LCM and GCF Find the Least Common Multiple (LCM). Using the standard and topic you choose from earlier this semester, write a full 45-minute lesson plan.
- https://math.libretexts.org/Courses/Western_Technical_College/PrePALS_PreAlgebra/02%3A_Fractions/2.04%3A_Adding_and_Subtracting_Fractions\[ \begin{aligned} \frac{4} + \frac{1}{6} &= \frac{4 \cdot \textcolor{red}{2}}{9 \cdot \textcolor{red}{2}} + \frac{1 \cdot \textcolor{red}{3}}{6 \cdot \textcolor{red}{3}} ~ & \textcolor{red}{ \text{ E...\[ \begin{aligned} \frac{4} + \frac{1}{6} &= \frac{4 \cdot \textcolor{red}{2}}{9 \cdot \textcolor{red}{2}} + \frac{1 \cdot \textcolor{red}{3}}{6 \cdot \textcolor{red}{3}} ~ & \textcolor{red}{ \text{ Equivalent fractions with LCD = 18.}} \\ &= \frac{8}{18} + \frac{3}{18} ~ & \textcolor{red}{ \text{ Simplify numerators and denominators.}} \\ &= \frac{8+3}{18} ~ & \textcolor{red}{ \text{ Keep common denominator; add numerators.}} \\ &= \frac{11}{18} ~ & \textcolor{red}{ \text{ Simplify numerator.}…
- https://math.libretexts.org/Courses/Mount_Royal_University/Higher_Arithmetic/4%3A_Greatest_Common_Divisor_least_common_multiple_and_Euclidean_Algorithm/4.3%3A_Least_Common_MultipleThe least common multiple , also known as the LCM, is the smallest number that is divisible by both integer a and b.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Raji)/02%3A_Prime_Numbers/2.04%3A_Least_Common_MultipleWe can use prime factorization to find the smallest common multiple of two positive integers.
- https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_(Arnold)/07%3A_Rational_Functions/7.05%3A_Sums_and_Differences_of_Rational_FunctionsIn this section we concentrate on finding sums and differences of rational expressions.
- https://math.libretexts.org/Bookshelves/Algebra/Elementary_Algebra_(Ellis_and_Burzynski)/01%3A_Arithmetic_Review/1.04%3A_The_Least_Common_MultipleWhen a whole number is multiplied by other whole numbers, with the exception of Multiples zero, the resulting products are called multiples of the given whole number. Notice that in our number line vi...When a whole number is multiplied by other whole numbers, with the exception of Multiples zero, the resulting products are called multiples of the given whole number. Notice that in our number line visualization of common multiples (above) the first common multiple is also the smallest, or least common multiple, abbreviated by LCM. The least common multiple, LCM, of two or more whole numbers is the smallest whole number that each of the given numbers will divide into without a remainder.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Barrus_and_Clark)/01%3A_Chapters/1.07%3A_Greatest_Common_Divisor_and_Least_Common_MultipleIn the last few chapters we have discussed divisibility and the Division Algorithm when a single number is divided by another. In this chapter we begin to look at divisors and multiples that two numbe...In the last few chapters we have discussed divisibility and the Division Algorithm when a single number is divided by another. In this chapter we begin to look at divisors and multiples that two numbers have in common.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/05%3A_Basic_Number_Theory/5.06%3A_Fundamental_Theorem_of_ArithmeticPrimes are positive integers that do not have any proper divisor except 1. Primes can be regarded as the building blocks of all integers with respect to multiplication.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/01%3A_Introduction_and_Notation/1.05%3A_Some_Algorithms_of_Elementary_Number_TheoryAn algorithm is simply a set of clear instructions for achieving some task. The Persian mathematician and astronomer Al-Khwarizmi1 was a scholar at the House of Wisdom in Baghdad who lived in the 8th...An algorithm is simply a set of clear instructions for achieving some task. The Persian mathematician and astronomer Al-Khwarizmi1 was a scholar at the House of Wisdom in Baghdad who lived in the 8th and 9th centuries A.D. He is remembered for his algebra treatise Hisab al-jabr w’al-muqabala from which we derive the very word “algebra,” and a text on the Hindu-Arabic numeration scheme.
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/03%3A_Exponents_Roots_and_Factorization_of_Whole_Numbers/3.05%3A_The_Least_Common_MultipleFor the GCF, we attach the smallest exponents to the common bases, whereas for the LCM, we attach the largest exponents to the bases. \(\begin{array} {ccll} {90} & = & {2 \cdot 45 = 2 \cdot 3 \cdot 15...For the GCF, we attach the smallest exponents to the common bases, whereas for the LCM, we attach the largest exponents to the bases. \(\begin{array} {ccll} {90} & = & {2 \cdot 45 = 2 \cdot 3 \cdot 15 = 2 \cdot 3 \cdot 3 \cdot 5 = 2 \cdot 3^2 \cdot 5} & {} \\ {630} & = & {2 \cdot 315 = 2 \cdot 3 \cdot 105 = 2 \cdot 3 \cdot 3 \cdot 35} & {= 2 \cdot 3 \cdot 3 \cdot 5 \cdot 7} \\ {} & \ & {} & {= 2 \cdot 3^2 \cdot 5 \cdot 7} \end{array}\)
