Problem 10 · 2014 Math Kangaroo
Easy
Number Theory
divisibilityfactorization
The circumference of the large wheel of a bicycle measures 4·2 m, and that of the small wheel 0·9 m. To begin with, the valves on both wheels are at the lowest point; then the bicycle moves off. After a few metres both valves are again at the lowest point at the same time. After how many metres does this happen for the first time?
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Answer: C — 12·6 m
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Hint 1 of 2
Both valves return to the bottom after a whole number of turns of each wheel.
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Hint 2 of 2
Find the least common multiple of the two circumferences.
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Approach: least common multiple of the wheel circumferences
- The distance must be a whole-number multiple of both 4.2 m and 0.9 m.
- Work in tenths of a metre: lcm(42, 9) = 126, so 12.6 m.
- Both valves are lowest again first at 12.6 m.
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