Given that a multiple of a number is any number that can be divided evenly by that number, it follows that 72 has a literally infinite number of multiples. Infinite number sequences cannot be listed in full, but the first few multiples in the sequence are 72, 144, 216, 288, 360 and 432.
One of the most commonly used multiples of 72 is, of course, 72 itself. The product of 72 x 1, 72, is the number of years that the U.S. Census restricts access to its records after collecting data. According to the Census Bureau, this rule was written into law in 1978 and is known as the 72-year Rule.
Another multiple of 72 is 144, the product of 72 x 2. This is the number of items in a gross, or a dozen dozens, and it is used extensively in shipping and logistics. It is also what is known as an "evil" number because 144, when rendered in binary code, has an even number of ones in its expression, according to Number Gossip.
Skipping ahead, 72 x 5 = 360, which is the number of degrees in a circle. It is also, not coincidentally, the number of days on the Babylonian calendar, as reported by Wolfram Research.