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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