What is the greatest possible length which can be used to measure exactly the…

Convert all lengths to centimeters:

• 8 m = 800 cm

• 4 m 20 cm = 420 cm

• 12 m 20 cm = 1220 cm

Find the greatest common divisor (GCD) of 800, 420 and 1220 using the Euclidean algorithm:

1. gcd(800, 420): 800 = 420 × 1 + 380

2. 420 = 380 × 1 + 40

3. 380 = 40 × 9 + 20

4. 40 = 20 × 2 + 0, so gcd(800, 420) = 20

5. Now gcd(20, 1220): 1220 is divisible by 20 (1220 = 20 × 61), so gcd(20, 1220) = 20

Therefore the greatest possible length that measures all three exactly is 20 cm.