What is the longest rod that can measure each of the lengths 2 1/2 m, 3 3/4 m and 5 m an exact whole number of times?

Write the lengths as fractions: 5/2, 15/4 and 5/1. For fractions the rule is HCF = (HCF of the numerators) ÷ (LCM of the denominators). Here HCF(5, 15, 5) = 5 and LCM(2, 4, 1) = 4, so the rod is 5/4 m = 1 1/4 m. Check: 5/2 ÷ 5/4 = 2, 15/4 ÷ 5/4 = 3 and 5 ÷ 5/4 = 4, all whole numbers. Swapping the two rules — LCM of the tops over HCF of the bottoms — gives 15 m, a "rod" longer than every length it is supposed to measure, which is the clue that the rules have been used the wrong way round.