common multiple Of 4 and 6

Question

common multiple of 4 and 6

Answer 1

The multiples of 4:      4,  8,  12,   16,   20,   24,   28,   32,   . . .

The multiples of 6:      6,   12,   18,   24,   30,   36,   . . .

 

The common multiples of 4 and 6 (see values in both lists):    12,   24,   ...

 

The least common multiple (LCM) of 4 and 6:  12

 

Now --

The prime factors of 4:    2*2

The prime factors of 6:    2*3

 

Include each term only once, the LCM of 4 and 6 is 2*2*3=12.

 

Note that 12 is divisible by 4 and 12 is divisible by 6.

Answer 2

If we are looking for the least common multiple of 4 and 6, we know that one potential solution is 4 x 6 = 24, because clearly 24/6 = 4 and 24/6 = 4. However, we notice from the prime factorization of 4 (2 x 2) and 6 (2 x 3) that they share a factor of 2. Thus, we know that when we multiply 4 and 6 to find a common multiple, we are repeating a factor of 2. Therefore, the least common multiple is 24/2 = 12.