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  2. Least common multiple - Wikipedia

    en.wikipedia.org/wiki/Least_common_multiple

    Here, the composite number 90 is made up of one atom of the prime number 2, two atoms of the prime number 3, and one atom of the prime number 5. This fact can be used to find the lcm of a set of numbers. Example: lcm(8,9,21) Factor each number and express it as a product of prime number powers.

  3. Lowest common denominator - Wikipedia

    en.wikipedia.org/wiki/Lowest_common_denominator

    Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers ...

  4. Table of prime factors - Wikipedia

    en.wikipedia.org/wiki/Table_of_prime_factors

    lcm(m, n) (least common multiple of m and n) is the product of all prime factors of m or n (with the largest multiplicity for m or n). gcd(m, n) × lcm(m, n) = m × n. Finding the prime factors is often harder than computing gcd and lcm using other algorithms which do not require known prime factorization.

  5. Greatest common divisor - Wikipedia

    en.wikipedia.org/wiki/Greatest_common_divisor

    The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.

  6. Chebyshev function - Wikipedia

    en.wikipedia.org/wiki/Chebyshev_function

    The second Chebyshev function is the logarithm of the least common multiple of the integers from 1 to ... (in these formulas p k is the k th prime number; p 1 = 2, p ...

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  8. Smooth number - Wikipedia

    en.wikipedia.org/wiki/Smooth_number

    Unlike n-smooth numbers, for any positive integer n there are only finitely many n-powersmooth numbers, in fact, the n-powersmooth numbers are exactly the positive divisors of “the least common multiple of 1, 2, 3, …, n” (sequence A003418 in the OEIS), e.g. the 9-powersmooth numbers (also the 10-powersmooth numbers) are exactly the ...

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