find the LCM and GCF by listing the prime factorizations of each

36 = 2*2*3*3

96 = 2*2*2*2*2*3

the LCM is each number the greates amount of times it appears.

2 appears 5 times and 3 appears 2 times

so the LCM is:

2*2*2*2*2*3*3 = 288

The GCF is the factors that are common in both lists

2 appears 2 times in both lists, 3 appears 1 time in both lists

so the GCF is:

2*2*3 = 12

the product of the LCM and GCF is when you multiply them together:

288*12 = 3456