You can decide if finding common multiples is useful if the question is asking for you to find out the next time multiples 2 numbers will ever be the same. You can decide if finding common factors is useful if the question is asking for you to divide 2 numbers equally. You will know to find the CM or CF because if it is asking you to divide, it is CF because it is going down and factors are smaller than the original number and if it is asking for you to multiply then it is CM because multiples are bigger.
2.
a.
To find the common factors of 2 numbers or CF, the easiest way would be to list all the factors of those 2 numbers so you can see which ones are common. To find the greatest common factor, or GCF, will also be very easy, you just take all the common factors and find the greatest one, the one with the highest value.
Example: 24 and 60 Bold = CF Underline = GCF
24 - 1, 2, 3, 4, 6, 8, 12, 24
60 - 1, 2, 3, 5, 6, 10, 12, 20, 30, 60
b.
The GCF of 2 numbers will give us a number to divide both numbers by and if we put them into groups the groups would be equal.
3.
a.
Finding the CM and LCM of 2 numbers is very much like finding the CF and GCF, all that's different is that you are listing multiples instead of factors. Of course, this list could go on forever, but no one would want to do that. To find the LCM, it is just the first common multiple you come across, if your listing them in order that is. Another way to find the LCM is that if the 2 numbers are both prime, you can just multiply them together.
Example #1: 24 and 60 Bold = CM Underline =LCM
24 - 24, 48, 72, 96, 120, 144, 168, 192, 226, 240
60 - 60, 120, 180, 240
Example #2: 5 and 17 (Both Prime)
17 * 5 = 85
The LCM of 2 numbers will tell us which number those 2 numbers have in common and also when those 2 numbers will meet. Also, even though you probably won't use this information, it gives us 2 factors of the LCM.
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