120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200, 1320, . . .
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108 and 120.
All multiples of 120 are multiples of both 40 and 24, because 120 contains all the factors of 40 (23*5) and 24 (23*3). Some examples of multiples are 120, 240, 360, and 600.
60 and 120
The multiples of 120 are mentioned in the first answer. The multiples for 120 are 2, 3 and 5. An alternative answer is 2, 3, 4, 5, 6, 10, 15, 20, 30 and 60. That is 10 numbers. There is no smaller number 120 that can be divided 10 or more times. This is probably why sumerians chose 60 (half of 120) and 360 (3 times 120) as common numbers.
There is an infinite number of common multiples for 40 and 60. A common multiple of any two numbers is any number into which each of two or more numbers can be divided evenly (zero remainder).