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?
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.