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Using prime factorization, determine the least common multiple of 10, 12, 14

Sagot :

To determine the least common multiple (LCM) of 10, 12, and 14 using prime factorization, we first need to find the prime factors of each number:

10: 10=2×5

12: 12=2^(2)×3

14: 14=2×7

Next, we identify the highest power of each prime number that appears in the factorizations:

Prime 2: The highest power is

2^(2)  (from 12).

Prime 3: The highest power is

3^(1)  (from 12).

Prime 5: The highest power is

5^(1) (from 10).

Prime 7: The highest power is

7^(1) (from 14).

The LCM is found by multiplying these highest powers together:

=2^(2)×3^(1)×5^(1)×7^(1)

Calculating this:

LCM=4×3×5×7

=>

LCM=12×5×7

=>

LCM=60×7

=>

LCM=420

So, the least common multiple of 10, 12, and 14 is 420.

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