lowest common multiple of 600 and 108

What you would do is find the multiples of each number first (besides 0). For 600, there is 600, 1200, 1800, 2400, 3000, 3600, 4000, etc.

And for 108: 108, 216, 324, 432, 540, 648, etc.

The lowest number that is included in both sets would be 5,400, therefore that is the LCM.

Excellent work anonymous4338 

Here is another way

$${factor}{\left({\mathtt{600}}\right)} = {{\mathtt{2}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}}$$

$${factor}{\left({\mathtt{108}}\right)} = {{\mathtt{2}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{3}}}$$

Include all factors but if the factor appears in both only include it once.

so lowest common multiple will be   $${{\mathtt{2}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}} = {\mathtt{5\,400}}$$