Using a method called “Euclid’s Algorithm” I will find the LCM and GCF of the numbers 425 and 187. First, let’s find the GCF, and then using that we can find the LCM.

First, divide the two numbers (the first number by the second number). 425 / 187 = 2 with a remainder of 51. From this, we can draw the conclusion that 425= 2 x 187 + 51

Next, divide the second number (187) and the remainder (51). 187 / 51 = 3 R 34. We can draw the conclusion that 187 =3 x 51+34.

Take the last part of the equation, (the first remainder, 51, and the second remainder, 34,) and divide those two together. Keep on doing this until you get a remainder of zero.

51/34= 1R 17 so 51= 1 x 34 +17

34/17= 2R 0 so 34= 2 x 17 + 0

So the GCF is 17.

To find the lowest common multiple, multiply the two original numbers.

425 x 187 = 79, 475

Then divide that by the GCF that we just found.

79, 475 / 17 = 4,675

The lowest common multiple of 425 and 187 is 4,675.

I prefer prime factorization, because with this method you need to find or be given the GCF first. Finding the GCF is difficult because it can get confusing when dealing with remainders and lots of equations. Finding the lowest common multiple is a lot easier because you just have to divide two numbers but finding the GCF is more complicated than just using the prime factorizations method.