What is the least common multiple of 8 and 12 ? lcm(8,12)=

Identify prime factorization of 8: Identify the prime factorization of 8. Prime factorization of 8: 2 × 2 × 2 (which is 2^3)Identify prime factorization of 12: Identify the prime factorization of 12. Prime factorization of 12: 2 × 2 × 3 (which is 2^2 × 3)Identify distinct prime factors: Identify all the distinct prime factors from the prime factorizations of both numbers. Distinct prime factors: 2, 3Choose highest power for each prime factor: For each distinct prime factor, choose the highest power of it that appears in either factorization. For 2, the highest power is 2^3 (from 8). For 3, the highest power is 3^1 (from 12).Multiply highest powers to find LCM: Multiply these highest powers together to find the least common multiple (LCM). Multiply 2^3 and 3^1 to find the LCM. 2^3 × 3^1 = 8 × 3 = 24 LCM of 8 and 12 is 24.

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Math Problems

Grade 6

Least common multiple of three or four numbers

Full solution

Q. What is the least common multiple of

8

and

12

\newline

\operatorname{lcm}(8,12)=

Identify prime factorization of $8$ : Identify the prime factorization of $8$ . $\newline$ Prime factorization of $8$ : $2 \times 2 \times 2$ (which is $2^3$ )
Identify prime factorization of $12$ : Identify the prime factorization of $12$ . $\newline$ Prime factorization of $12$ : $2 \times 2 \times 3$ (which is $2^2 \times 3$ )
Identify distinct prime factors: Identify all the distinct prime factors from the prime factorizations of both numbers. $\newline$ Distinct prime factors: $2$ , $3$
Choose highest power for each prime factor: For each distinct prime factor, choose the highest power of it that appears in either factorization. $\newline$ For $2$ , the highest power is $2^3$ (from $8$ ). $\newline$ For $3$ , the highest power is $3^1$ (from $12$ ).
Multiply highest powers to find LCM: Multiply these highest powers together to find the least common multiple (LCM). $\newline$ Multiply $2^3$ and $3^1$ to find the LCM. $\newline$ $2^3 \times 3^1 = 8 \times 3 = 24$ $\newline$ LCM of $8$ and $12$ is $24$ .