Question

What is the least number of chairs needed for an auditorum so that they can be
arranged either 27 in a row or 33 in a row?​

Answer 1

The number of chairs will need to be a multiple of 27 (so they can have “m” rows of 27 chairs each, for a total of 27m chairs) and also a multiple of 33 (so they can have “n” rows of 33 chairs each, for a total of 33n chairs).

What is the least common multiple (LCM) of 27 and 33?

If you set 27m equal to the LCM, what value do you get for “m”? (This is the number of 27-chairs-each rows you can get.)

If you get 33n equal to the LCM, what value do you get for “n”? (This is the number of 33-chairs-each rows you can get.)

Note: This is only the SMALLEST number of chairs for which you can set up the chairs in the stipulated manner. Any multiple of the LCM will work, also.

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