Answer:
a number into which each number in a given set may be evenly divided.
Step-by-step explanation:
for example
the least common multiple of 3 and 4 would be 12
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):
[tex]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}\\[/tex]
where some of the [tex]p_x[/tex] and [tex]p_y[/tex] overlap (are equal). Then, you find the largest exponent of each [tex]p_i[/tex] and multiply them together. For example:
34 and 82
[tex]34 = 2^1\cdot17^1\\24 = 2^3\cdot3^1\\lcm[34,24] = 2^3\cdot3^1\cdot17^1[/tex]
Notice how multiplying the 2 numbers will yield a common multiple, but not the lcm.
