# Question #8d992

Nov 10, 2017

168.

#### Explanation:

Use the picture I've created (linked):

Nov 11, 2017

The least common factor is 168.

#### Explanation:

The prime factorization method is the fastest for sure! However, another way to answer or look at this question is to briefly examine what LCM stands for. The Least Common Multiple says find all the multiples of 8, 7, and 12 and then find the least or smallest one that is common to all three numbers.

The multiples of 8 are:
$8 , 16 , 24 , 32 , 40 , 48 , 56 , 64 , 72 , 80 , 88 , 96 , 104 , 112 , 120 , 128 , \ldots$

The multiples of 7 are:
$7 , 14 , 21 , 28 , 35 , 42 , 49 , 56 , 63 , 70 , 77 , 84 , 91 , 98 , 105 , 112 , \ldots$

The multiples of 12 are:
$12 , 24 , 36 , 48 , 60 , 72 , 84 , 96 , 108 , 120 , 132 , 144 , 156 , \textcolor{red}{168} , 180 , \ldots$

With this small list, none of the multiples is common to all three. Looking at a few more, we get:

The (additional) multiples of 8 are:
$\ldots , 136 , 144 , 152 , 160 , \textcolor{red}{168} , \ldots$

The (additional) multiples of 7 are:
$\ldots , 119 , 126 , 133 , 140 , 147 , 154 , 161 , \textcolor{red}{168} , \ldots$

The least common factor is therefore 168.