That's a bit of unnecessary work. The LCM of 3 and 6 is 6, because 6 is a multiple of 3.
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Oh, dude, the LCM of 12 and 15 using a Venn diagram? That's like trying to use a spoon to eat soup, it just doesn't quite fit. But hey, if you really wanna know, the LCM of 12 and 15 is 60. Just think of it as the magical number where 12 and 15 finally decide to hold hands and skip down the number line together.
To find the GCF and the LCM you have to first at least try to use prime factorization. So use factor trees. Or for the LCM find th least common multiples of the number.
I've never found Venn diagrams all that useful. To draw one successfully, you already have to know the answer. But here goes... Example: 30 and 42 30, 60, 90, 120, 150, 180, 210 42, 84, 126, 168, 210 These are lists of multiples of 30 and 42 respectively, that would be placed in two circles. The number 210 would be placed in the center where they intersect.
The LCM is: 117
The LCM is: 120