Question

I need some help in my homework and it is what is a common multiple

Answer 1

Given numbers x and y, their common multiple is any number that has both x and y as factors or divisors. You can find the least common multiple (LCM) of two numbers by finding their prime factorization (using p_k for demonstration purposes):

`x = p_1^(e_1)p_3^(e_3)...p_k^(e_k)\\y = p_2^(e_2)p_4^(e_4)...p_n^(e_n)\\`

where some of the
`p_x` and
`p_y` overlap (are equal). Then, you find the largest exponent of each
`p_i` and multiply them together. For example:

34 and 82

`34 = 2^1\cdot17^1\\24 = 2^3\cdot3^1\\lcm[34,24] = 2^3\cdot3^1\cdot17^1`

Notice how multiplying the 2 numbers will yield a common multiple, but not the lcm.

Answer 2

a number into which each number in a given set may be evenly divided.

Explanation:

for example

the least common multiple of 3 and 4 would be 12