MHB -c03 write prime factorization of the LCM of A and B

[karush]

Build the least common multiple of A and B
a. write the prime factorization of the least common multiple of A and B.
$A=2\cdot 3^2\cdot 5\cdot 7^3\cdot 11^3\cdot 13^2$
$B= 3^2 \cdot 5 \cdot 7^2 \cdot 11^2$
$\dfrac{2\cdot \cancel{3^2}\cdot \cancel{5\cdot 7^2} 7\cdot \cancel{11^2} 11\cdot 13^2}
{\cancel{3^2} \cdot 5 \cancel{\cdot 7^2} \cdot \cancel{11^2}}
=2\cdot 7\cdot 11\cdot 13^2=26026$

not sure if I went the right direction on this how do we get the prime factorization

 

[skeeter]

The LCM would be …

$2 \cdot 3^2 \cdot 5 \cdot 7^3 \cdot 11^3 \cdot 13^2$

The GCF would be …

$3^2 \cdot 5 \cdot 7^2 \cdot 11^2$

 

[karush]

so its not A and B together? altho B is subset of A

 

[skeeter]

LCM is A times B (together) only if A and B are relatively prime