Find the LCM by using the factorization method.

a. 12, 18, 27

b. 10, 12, 20

To find the Least Common Multiple (LCM) of the given numbers using the factorization method, we first need to find the prime factors of each number.
a. LCM of 12, 18, 27

Find the prime factors of each number:

12: 12 = 2 2 × 3 1
18: 18 = 2 1 × 3 2
27: 27 = 3 3


Identify the highest power of each prime number that appears in the factorizations:

For 2, the highest power is 2 2 (from 12).
For 3, the highest power is 3 3 (from 27).


Multiply these highest powers together to find the LCM: LCM = 2 2 × 3 3 = 4 × 27 = 108


So, the LCM of 12, 18, and 27 is 108.
b. LCM of 10, 12, 20

Find the prime factors of each number:

10: 10 = 2 1 × 5 1
12: 12 = 2 2 × 3 1
20: 20 = 2 2 × 5 1


Identify the highest power of each prime number that appears in the factorizations:

For 2, the highest power is 2 2 (from 12 and 20).
For 3, the highest power is 3 1 (from 12).
For 5, the highest power is 5 1 (from 10 and 20).


Multiply these highest powers together to find the LCM: LCM = 2 2 × 3 1 × 5 1 = 4 × 3 × 5 = 60


Therefore, the LCM of 10, 12, and 20 is 60.

Answered by IsabellaRoseDavis | 2025-07-21

The LCM of 12, 18, and 27 is 108, and the LCM of 10, 12, and 20 is 60. This is determined using the prime factorization method, where we find the highest powers of prime factors from each number. By multiplying these highest powers together, we obtain the least common multiples.
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Answered by IsabellaRoseDavis | 2025-08-06