Find the length of the longest rod which can be used to measure exactly the lengths 5 m 13 cm, 11 m 34 cm and 12 m 15 cm.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 27 cm
A rod can measure a length with no part left over only when it fits into it a whole number of times, so the longest such rod is the HCF of the three lengths, all taken in the same unit.
5 m 13 cm \(=513\) cm \(=3^3\times19\)
11 m 34 cm \(=1134\) cm \(=2\times3^4\times7\)
12 m 15 cm \(=1215\) cm \(=3^5\times5\)
HCF \(=3^3=27\) cm (the only common factor is 3, and its lowest power is \(3^3\))