Can you guys give me the least common multiple of 60.24 and 65.16. Please and thank you.
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1 Answer

60.24=4×15.06; 65.16=4×16.29.

It's unusual to find LCMs of fractions but in this case both numbers go into:

4×15.06×16.29=981.3096.

This problem suggests a different problem such as synchronisation of two close measurements of distance or time. For example: two frequencies or wavelengths. The technique for finding out when two wavelengths initially in sync will be in sync again is different from findling the LCM. In such cases the difference between the two measurements is calculated: 4.92.

Consider two sticks, one of length 60.24 and the other of length 65.16. If the two sticks are aligned at one end, the larger stick will be 4.92 units longer than the shorter one. Imagine two set of sticks, A and B, one set consisting of 60.24 lengths, the other set consisting of 65.16 lengths. If each stick in its set is numbered then A1, A2, A3, ... is placed end to end in a line and similarly for B1, B2, B3, ..., the leading end of B1 will be 4.92 units ahead of the leading end of A1, and B2 will be 9.84 units ahead of A2, and so on. Eventually Bn stick will be so far ahead of the corresponding An stick that it will have caught up with An+1.

This will happen when this equation is solved: 60.24(n+1)=65.16n, 60.24n+60.24=65.16n, n=60.24/4.92=12.24.

This tells us that 13 A sticks are almost aligned to 12 B sticks.

Synchronisation occurs every 12.24 units, and the units could be seconds, so two sound waves of similar frequencies would produce beats at a lower frequency, that is, a longer wavelength related to the number 12.24.

by Top Rated User (1.1m points)

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