Mathematics - Number Theory - GCD and LCM - The Garden Tile Problem

Show a rectangular garden that is 12m × 8m. The gardener wants to tile it with identical square tiles with NO cutting. What is the LARGEST square tile that works? Student tries different sizes: 1m works but tiny, 2m works, 3m doesn't (8/3 not integer), 4m works perfectly! 4 is the GCD(12,8). Visual:

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Mathematics - Number Theory - GCD and LCM - The Garden Tile Problem
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Mathematics - Number Theory - GCD and LCM - The Garden Tile Problem

vivmagarwal
vivmagarwalJan 29, 2026

Description

Show a rectangular garden that is 12m × 8m. The gardener wants to tile it with identical square tiles with NO cutting. What is the LARGEST square tile that works? Student tries different sizes: 1m works but tiny, 2m works, 3m doesn't (8/3 not integer), 4m works perfectly! 4 is the GCD(12,8). Visual:

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MathematicsNumber TheoryClass 6, Class 6, Stage 7, Grade 6, MYP Grade 7

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