As loudly as one can. I've hardly slept because my infant has been crying at the top of her lungs all night.Sing at the top of your lungs so that the people in the last row of the auditorium can hear you!Kids, can you please stop screaming at the top of your lungs?
Also, at the top of one's voice. With an extremely loud voice. For example, The babies in the nursery all were crying at the top of their lungs. The noun top here refers to the greatest degree of volume (that is, loudest) rather than high pitch, a usage dating from the mid-1500s.
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