The new way I found to find LCM/GCF is involving listing all the multiples of the number. So, if you are trying to find the LCM of 100 and 102 the first step would be to list out the multiples of 100 starting with 100 * 1. Now since we are dealing with big numbers we can see using calculator that the LCM will be 5100, so instead of listing out all the multiples starting from multiplying by 1 we can multiply by 40.
step 1: 100 * 40 = 4000 step 2: 102 * 40 = 4080
100 * 41 = 4100 102 * 41 = 4182
100 * 42 = 4200 102 * 42 = 4284
100 * 43 = 4300 102 * 43 = 4386
100 * 44 = 4400 102 * 44 = 4488
100 * 45 = 4500 102 * 45 = 4590
100 * 46 = 4600 102 * 46 = 4692
100 * 47 = 4700 102 * 47 = 4794
100 * 48 = 4800 102 * 48 = 4896
100 * 49 = 4900 102 * 49 = 4998
100 * 50 =5000 102 * 50 = 5100
100 * 51 =5100
since 5100 is the lowest multiple both numbers have it is the LCM.
To find the GCF you must find the factors of 100 and 102.
100= 1, 2,4,5,10,20,25,50
102= 1,2,3,6,17,34,51,102
Since the greatest factor both 100 and 102 share is 2 the GCF is 2.
After searching up this new method I still prefer the one we were taught in class because it is way faster and more simple for me to understand.