Page 26 - Numbertheory

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[Least Common Multiple]

lcm (a,b ) ba

m : .b a
.a  m
.m ≤n n >0 am( )
bn an ()

: gcd(a, b ) . lcm (a, b ) = ab
()

. gcd(45, 75) = 15 ( ) ()

. lcm (45, 75) = 45× 75 = 225

15

:

lcm (a1, a2, ... , an ) = lcm (a1, a2, ... , an−2 , lcm (an−1, an ))

75 45 35 ()

.( ( ) ) lcm (45, 75) = 225

lcm (35, 45,75) = lcm (35, 225)

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