Respuesta :

Answer:

48

Step-by-step explanation:

12 : (12, 24, 48)

16: ( 16,32, 48)

Answer: 48

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Method #1

Multiply the two values to get 12*16 = 192

Then divide over the GCF 4 getting 192/4 = 48

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Method #2

List out the multiples of each and see what they have in common

Multiples of 12 = {12, 24, 36, 48, 60, 72, 84, 96, ...}

Multiples of 16 = {16, 32, 48, 64, 80, 96, ...}

We see that 48 is the smallest common multiple.

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Method #3

Find the prime factorization for each

12 = 2*2*3

16 = 2*2*2*2

The unique prime factors are 2 and 3

The prime 2 shows up at most 4 times, so 2^4 = 16 is one factor of the LCM

The prime 3 shows up at most 1 time, so 3^1 = 3 is the other factor of the LCM

The LCM is 3*16 = 48.