First things first, I got the picture to appear upright!
We are still working on Prime Factorization and using the prime factors of two numbers to find GCF and LCM. I have shown one method of finding the prime factorization of both 30 and 75. This is the tree method. Once all the primes have been found, you can create the Prime Factorization. 30=2x3x5 and 75=3x5x5
Then, we create the Venn Diagram. Where the circles overlap in the middle, the prime numbers shared by the two numbers are placed; so with 30 and 75, 3 and 5 are shared and go in the center (or overlap) section. The 2 that is left from 30 belongs in the outer (non-shared) section of the 30 circle. The 5 that is left from the 75 belongs in the outer (non-shared) section of the 75 circle. If you multiply the two shared primes - 3x5 - you have the GCF of the two numbers.
To find the LCM, all the factors in the Venn Diagram are multiplied. Example: 3x5 (the GCF) as well as the 2 that is in 30 section and the 5 that is in the 75 section or 2x3x5x5. This equals 150, which is the Least Common Multiple of 30 and 75.
We are still working on Prime Factorization and using the prime factors of two numbers to find GCF and LCM. I have shown one method of finding the prime factorization of both 30 and 75. This is the tree method. Once all the primes have been found, you can create the Prime Factorization. 30=2x3x5 and 75=3x5x5
Then, we create the Venn Diagram. Where the circles overlap in the middle, the prime numbers shared by the two numbers are placed; so with 30 and 75, 3 and 5 are shared and go in the center (or overlap) section. The 2 that is left from 30 belongs in the outer (non-shared) section of the 30 circle. The 5 that is left from the 75 belongs in the outer (non-shared) section of the 75 circle. If you multiply the two shared primes - 3x5 - you have the GCF of the two numbers.
To find the LCM, all the factors in the Venn Diagram are multiplied. Example: 3x5 (the GCF) as well as the 2 that is in 30 section and the 5 that is in the 75 section or 2x3x5x5. This equals 150, which is the Least Common Multiple of 30 and 75.