Question 1140911

if the {{{LCM }}}of {{{a}}} and {{{b}}} is {{{12}}},

the set of primes that could be {{{a}}} and {{{b}}} is:

{{{12=1*2*2*3}}}



 and, if the {{{LCM}}} of{{{ b}}} and {{{c}}} is {{{15}}}. the set of primes that could be {{{b}}} and {{{c}}} is:

{{{15=1*3*5}}}

What is the value of the LCM of a and c?

The {{{LCM}}}({{{a}}},{{{c}}}) is calculated by finding the prime factorization of both {{{a}}} and {{{c}}} then taking the product of the sets of primes with the highest exponent value among {{{a}}} and {{{c}}}.

from above, we know that the sets of primes of {{{a}}} and {{{c}}} could be:

{{{a}}}=>{{{1*2*2*3}}}
and 
{{{c}}}=>{{{1,3,5}}}


both have in common {{{1,3}}}=> so {{{ a=1}}} and {{{c=3}}}, or{{{ a=3}}} and {{{c=1}}}

so, the {{{LCM }}}of {{{a}}} and{{{ c}}}: is{{{ 3}}}