Least Common Multiples vs. Greatest Common Factors (LCM vs. GCF) | Math with Mr. J

Mr. J introduces the video, explaining that it will cover the difference between greatest common factors (GCF) and least common multiples (LCM). He mentions a more in-depth video on factors and multiples in the description. The video will proceed with two examples to illustrate the concepts.

The first example involves finding the LCM for 12 and 9. Mr. J explains that multiples are found by multiplying the number by integers. He lists the first few multiples of 12 (12, 24, 36, 48, 60) and then 9 (9, 18, 27, 36, 45). The least common multiple identified is 36, as it is the smallest value shared by both lists.

Next, the video shifts to finding the GCF for 12 and 9. Factors are defined as numbers that can divide the given number evenly or numbers that can be multiplied to get the given number. Mr. J lists factors of 12 (1, 2, 3, 4, 6, 12) and 9 (1, 3, 9). He then identifies the greatest common factor as 3.

The second example starts with finding the LCM for 20 and 15. The multiples for 20 are listed as 20, 40, 60, 80, 100. The multiples for 15 are 15, 30, 45, 60. The least common multiple is found to be 60.

Finally, the video covers the GCF for 20 and 15. The factors of 20 are 1, 2, 4, 5, 10, 20. The factors of 15 are 1, 3, 5, 15. The greatest common factor shared by both numbers is determined to be 5.