Answer :

What you're discussing here is prime factorization (or turning a number into the multiples of its prime numbers).  18 becomes 2*3*3.  48 becomes 2*2*2*2*3. They share one 2 and one 3 in those prime factors.  Which is why 6 is their least common multiple (or LCM).  Because, 2*3 = 6.
lcm=least common multiplule

factor
18=2*3*3
48=2*2*2*2*3

we need to have at least two 3's and four 2's
lcm=2*2*2*2*3*3=144

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