Page 27 - Numbertheory

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225 = 6×35 +15

35 = 2×15 + 5

15 = 3×5 + 0

. lcm (35, 225) = 35 × 225 = 1575
5

. lcm (35, 45, 75) = 1575

. lcm (6, 10,15) = 30 ()

gcd(6, 10, 15) = 1

lcm (6,10, 15)gcd(6, 10,15)= 30 ≠ 6×10×15 = 900

. ba ()
.
yx
1 = ax + by

. gcd(a,b ) = 1

1 = ax + by

.d =1 .d b d a . gcd(a,b ) = d > 1
. d 1 .d  (ax +by )

. ab  c bc ac gcd(a,b ) = 1 ()

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