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That would be a number line.
The LCM will never be less than the GCF. To be a multiple of both numbers, the LCM will have to be equal to or greater than the larger number. To be a factor of both numbers, the GCF will have to be equal to or less than the smaller number. The only problem comes when you're comparing a number to itself. The LCM of 10 and 10 is 10. The GCF of 10 and 10 is 10.
The Sieve of Erastosthenes shows prime numbers.
To find the GCF of 36, 42, and 54, we must find the prime factors of all of the 3 numbers. 36=12*3=4*3*3 42=6*7=2*3*7 54=6*9=2*3*3*3 For the GCF, you must include any number that is a factor of EVERY number in the list, and you write it the least amount of times that it shows up. Only 2 and 3 are factors of all three of the numbers you listed. The least 2 shows up is 1 time, and the least 3 shows up is one time. So the GCF is 2*3=6
84 = 2*2*3*7