Oh, isn't that just lovely! To find the common multiples of 2, 5, and 9, we can start by listing the multiples of each number. For 2, we have 2, 4, 6, 8, 10, and so on. For 5, we have 5, 10, 15, 20, and so forth. And for 9, we have 9, 18, 27, 36, and on it goes. The common multiples are the numbers that appear in the list of multiples for all three numbers, such as 90 and 180. Just like painting a happy little tree, finding common multiples can be a peaceful and joyful process.
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To find the common multiples of 2, 5, and 9, we first list the multiples of each number. The multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... The multiples of 5 are 5, 10, 15, 20, 25, 30, ... The multiples of 9 are 9, 18, 27, 36, ... The common multiples of 2, 5, and 9 are the numbers that appear in all three lists, which are the multiples of the least common multiple (LCM) of 2, 5, and 9. The LCM of 2, 5, and 9 is 90, so the common multiples are 90, 180, 270, ...
There is an infinite number of common multiples for 2 and 10. A common multiple of any two or more numbers is any number into which each of two or more numbers can be divided evenly (zero remainder). However, the least or lowest common multiple of 2 and 10 is 20.
There is an infinite number of common multiples for 2 8 and 10. A common multiple of any two or more numbers is any number into which each of two or more numbers can be divided evenly (zero remainder). However, the least or lowest common multiple (LCM) of 2 8 and 10 is 40.
The common multiples of 2, 5, and 9 are the infinite set of multiples of their LCM, which is 90. So the set begins 90, 180, 270, 360, 450, 540, 630, 720, 810, 900, and so on.
The first 5 common multiples are the first 5 multiples of their lowest common multiple (LCM) LCM(9, 10) = 90 → first 5 common multiples are 90, 180, 270, 360, 450.
LCM = 9x5x2 = 90 all multiples are 90, 180, 270, etc
315
18
All nonzero numbers have multiples. Some numbers have some of the same multiples as other numbers. These are known as common multiples. 36 is a multiple of 4. 36 is a multiple of 9. 36 is a common multiple of 4 and 9.