If we have two positive integers where one is greater than the other, which quantity would be greater (if possible): the larger integer divided by the smaller, or the result of dividing the least common multiple by the greatest common factor of the two integers? Since every number is both a divisor of itself and a multiple of itself, I know that the least common multiple could be the greater of the two integers at the least, and that the greatest common factor could be the lesser of the two integers at the most. Otherwise, the least common multiple at most could be the multiplication of the two integers divided by the greatest common factor. What would be the METHOD we would use to reason the relationship between the quantities?
If we have two positive integers where one is greater than the other, which quantity would be greater (if possible): the larger integer divided by the smaller, or the result of dividing the least common multiple by the greatest common factor of the two integers? Since every number is both a divisor of itself and a multiple of itself, I know that the least common multiple could be the greater of the two integers at the least, and that the greatest common factor could be the lesser of the two integers at the most. Otherwise, the least common multiple at most could be the multiplication of the two integers divided by the greatest common factor. What would be the METHOD we would use to reason the relationship between the quantities?
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