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Question
Find the length of the plank that can be used to measure the lengths 4 m 20 cm and 5 m 4 cm exactly, in the least time.
Sum
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Solution
Convert both lengths into centimetres
4 m 20 cm = 4 × 100 + 20 = 420 cm
5 m 4 cm = 5 × 100 + 4 = 504 cm
Prime factors of 420 = 2 × 2 × 3 × 5 × 7
= 22 × 3 × 5 × 7
Prime factors of 504 = 2 × 2 × 2 × 3 × 3 × 7
Common factors = 23 × 32 × 7
= 4 × 3 × 7
= 84
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