show me the first three common factors of 6,9,10

find the LCM of 6, 9, and 10

first write each number as a product of prime factors

6=2x3

9=3x3

10=2x5

to be a multiple of 6, the LCM must contain all of the prime factors of 6

LCM=2x3

*so far*to be a multiple of 9, the LCM must contain all of the prime factors of 9, but we don't use those prime factors that we already have(we want the

*least*common multiple)we need two 3's but we already have one 3 so we take only one 3 from 9

LCM=2x3x3

*so far*to be a multiple of 10, the LCM must contain all of the prime factors of 10, but we don't use those prime factors that we already have

we need a 2 and a 5 but we already have the 2 so we take the 5 only from 10

LCM=2x3x3x5=90

the next common multiples will be multiples of 90: 180, 270, 360...

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