- printf: documentation ( source)
<?php
$startLM = new DateTime('first day of previous month', new DateTimeZone('America/Detroit'));
$startLM->modify('today');
$startLM->setTimezone(new DateTimeZone('UTC'));
$startLastMonth = $startLM->format('Y-m-d H:i:s');
$endLM = clone $startLM;
$endLM->modify('+30 day');
$endLM->modify('+1 day');
$endLastMonth = $endLM->format('Y-m-d H:i:s');
printf('`timestamp` >= %s AND `timestamp` < %s', $startLastMonth, $endLastMonth);