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Status: Tags: Links: Integers

Least Common Multiple

Principles

• A positive integer c is called a common multiple of integers a and b if ;; a | c and b | c

• Number c is the lcm(a,b) if ;; for any common multiple d we have c | d

Theorem

Find lcm(231, 455) brute force method ?

• 231 = 3(77) = 3(7)(11)
• 455 = 5(91) = 5(7)(13)
• lcm(231,455) = 3(7)(11)(5)(13)
  • Don’t count duplicates, consider highest degree

For any integers a and b, the least common multiple exists where ab = ;; lcm (gcd(a,b))

Find lcm(231,455) using theorem ?

• lcm(a,b) = (ab)/(gcd(a,b))
• Find gcd which is 7
• lcm(a,b) = (231 x 455)/7 =

Backlinks

1

list from Least Common Multiple AND !outgoing(Least Common Multiple)

References:

Created:: 2021-11-29 20:35