Numbers & Operations
Multiples, Multiples, Multiples
Keep in mind that mathematicians are a literal bunch. So if you come across a concept called multiples, you can guess that multiplication is going to play a big part in it.
The multiples of an integer are the product of that integer and another integer. Consider the number 7. Some multiples of 7 are:
If you have two different numbers, you may be asked to find the least common multiple (LCM) the two numbers share. The LCM of two numbers is defined as the smallest integer that is a multiple of both numbers. Sometimes the LCM is simply the two numbers multiplied together. The LCM of 7 and 5 is 35, for instance. This is because 7 and 5 are both prime numbers. However, the LCM of 12 and 10 is not 120. To find the LCM of these two numbers, we have to run some numbers through the factor machine:
Multiples of 10 Multiples of 12
10 12
20 24
30 36
40 48
50 60
60 72
70 84
80 96
90 108
100 120
110
120
Can you see a number less than 120 that both numbers have in common? If you don’t, you must have some vision problem that makes the number 60 invisible to you. 60 is the LCM of 10 and 12.
There’s a complicated mathematical method to determine LCM, and there’s the way shown above. On the SAT, take the easy route.
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