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PLOTS OF GCD, LCM, REMAINDER, AND QUOTIENT Below are 3D plots of the greatest common divisor, least common multiple, remainder, and integer quotient functions of nonnegative integers x and y. These plots were produced by Mathematica. For each function, two plots are shown, one for a word size of three bits and the other for a word size of five bits. This material was suggested by Guy Steele. 8 32 6 y 24 8 4 2 4 24 8 16 x 2 0 32 y 16 6 8 0 0 x 0 FIGURE 1. Plots of the greatest common divisor function GCD(x, y). 8 32 6 y 24 8 4 y 6 2 0 24 8 4 2 32 16 16 x 8 0 0 x 0 FIGURE 2. Plots of the least common multiple function LCM(x, y). In Figure 2, the vertical scales are compressed; the highest peaks in the left figure are of height LCM(6, 7) = 42. 1 32 8 24 6 y 8 4 4 2 32 y 16 6 24 16 8 x 2 x 8 0 0 FIGURE 3. Plots of the remainder function rem(x, y). 2 8 4 8 6 6 32 y 16 24 4 x 24 16 8 2 x 8 0 32 0 FIGURE 4. Plots of the integer quotient function x÷y. Figure 4 is shown from a viewpoint different from that of the other figures. 2 y