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Find the LCM of 12 and 27 using prime factorizations​

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Answer:

108.

Step-by-step explanation:

Least common multiple (LCM) of 12 and 27 is 108.

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Step-by-step explanation:

Prime Factorization of 12

2 12

2 6

3 3

1

Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:

12 = 22×31

Prime Factorization of 27

3 27

3 9

3 3

1

Prime factors of 27 are 3. Prime factorization of 27 in exponential form is:

27 = 33

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 27.

LCM(12,27) = 22×33

LCM(12,27) = 108

Factors of 12

List of positive integer factors of 12 that divides 12 without a remainder.

1, 2, 3, 4, 6, 12

Factors of 27

List of positive integer factors of 27 that divides 27 without a remainder.

1, 3, 9, 27

Least Common Multiple of 12 and 27 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 12 and 27, than apply into the LCM equation.

GCF(12,27) = 3

LCM(12,27) = ( 12 × 27) / 3

LCM(12,27) = 324 / 3

LCM(12,27) = 108

Least Common Multiple of 12 and 27 by Listing Multiples

Multiples of 12

12, 24, 36, 48, 60, 72, 84, 96,108

Multiples of 27

27, 54, 81,108

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 12 and 27 is 108

Properties of LCM 12 and 27

(i) The LCM of 27 and 12 is associative

LCM of 12 and 27 = LCM of 27 and 12

Frequently Asked Questions on LCM of 12 and 27

1. What is the LCM of 12 and 27?

Answer: LCM of 12 and 27 is 108.

2. What are the Factors of 12?

Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.

3. What are the Factors of 27?

Answer: Factors of 27 are 1, 3, 9, 27. There are 4 integers that are factors of 27. The greatest factor of 27 is 27.

4. How to Find the LCM of 12 and 27?

Answer:

Least Common Multiple of 12 and 27 = 108

Step 1: Find the prime factorization of 12

12 = 2 x 2 x 3

Step 2: Find the prime factorization of 27

27 = 3 x 3 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 108 = 2 x 2 x 3 x 3 x 3

Step 4: Therefore, the least common multiple of 12 and 27 is 108.

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