Which greatest possible length can be used to measure exactly 15 meter 75 cm,…

Convert to centimeters: convert all lengths to cm.

• 15 m 75 cm = 1575 cm

• 11 m 25 cm = 1125 cm

• 7 m 65 cm = 765 cm

Find the greatest common divisor (GCD): use the Euclidean algorithm on 1575, 1125 and 765.

1. gcd(1575, 1125): 1575 − 1125 = 450 → gcd(1125, 450)

2. gcd(1125, 450): 1125 − 2×450 = 225 → gcd(450, 225)

3. gcd(450, 225): 450 − 2×225 = 0 → gcd(1575,1125) = 225

4. Now gcd(225, 765): 765 − 3×225 = 90 → gcd(225, 90)

5. 225 − 2×90 = 45 → gcd(90, 45)

6. 90 − 2×45 = 0 → gcd(1575,1125,765) = 45

Answer: The greatest length that measures all three exactly is 45 cm.