A quality control inspector in an egg factory checks every forty eighth egg for cracks and every fifty fourth egg for weight. What is the number of the first egg each day that the inspector check for both qualities?

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- March 7th 2007, 05:00 PMdiamond1smallest number
A quality control inspector in an egg factory checks every forty eighth egg for cracks and every fifty fourth egg for weight. What is the number of the first egg each day that the inspector check for both qualities?

- March 7th 2007, 09:27 PMCaptainBlack
You need the lowest common multiple of 48 and 54. Use whatever method

you have been shown to find this.

One way is to use the prime decompositions of the two numbers: 48=2^4*3, and 54=2*3^3, so lcm(48,54)= 2^4*3^3 = 432

So it is the 432nd egg that is checked for both qualities.

RonL - March 21st 2007, 04:08 PMmini
yes 432 is correc i tried a different method and it still worked. i wrote down all the eggs checked for cracks and all the eggs checked for weight until one matched