"the smallest positive integer that is divisible by both a and b."
The smallest number that is a multiple of two or more given numbers.
Factors and Multiples: Understanding the concept of factors and multiples is crucial when learning about the least common multiple. Factors are numbers that divide another number without remainder, and multiples are numbers that result from multiplying a number by any other number.
Prime Factorization: Prime factorization is the process of breaking down a composite number into its prime factors. This is useful when finding the LCM of two or more numbers.
Divisibility Rules: Divisibility rules are shortcuts used to determine whether a number is divisible by another number or not. These rules are crucial when finding the LCM of two or more numbers.
GCD and LCM: The greatest common divisor (GCD) is the largest number that divides two or more numbers without remainder. The least common multiple (LCM) is the smallest multiple that is common to two or more numbers. Understanding the relationship between GCD and LCM is important when finding the LCM of two or more numbers.
LCM using Prime Factorization: This is a common method used to find the LCM of two or more numbers. It involves finding the prime factors of each number, and then multiplying the highest power of each prime factor together.
LCM using the Division Method: This method involves finding the LCM of two or more numbers by dividing each number by its common factors until no more common factors can be divided.
LCM and Fractions: Understanding how LCM works with fractions is important when dealing with certain types of problems involving fractions, such as adding and subtracting fractions with unlike denominators.
Solving Real-World Problems using LCM: Knowing how to apply LCM to real-world problems is crucial when solving mathematical problems in fields such as finance, economics, and engineering.
"This definition has meaning only if a and b are both different from zero."
"Some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0."
"The least common multiple of the denominators of two fractions is the 'lowest common denominator' (lcd), and can be used for adding, subtracting or comparing the fractions."
"The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm(a, b, c, . . .), is defined as the smallest positive integer that is divisible by each of a, b, c, . . ."
"usually denoted by lcm(a, b)."
"A common multiple of two integers a and b."
"the smallest positive integer that is divisible by both a and b."
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"Some authors define lcm(a, 0) as 0 for all a, since 0 is the only common multiple of a and 0."
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"In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b."
"The least common multiple of the denominators of two fractions is the 'lowest common denominator' (lcd), and can be used for adding, subtracting or comparing the fractions."
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"The least common multiple of more than two integers a, b, c, . . . , usually denoted by lcm(a, b, c, . . .), is defined as the smallest positive integer that is divisible by each of a, b, c, . . ."
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