What is the least common multiple of 12 and 2 ? lcm(12,2)=

Identify prime factorization of 12: Identify the prime factorization of 12. Prime factorization of 12: 2 × 2 × 3Identify prime factorization of 2: Identify the prime factorization of 2. Prime factorization of 2: 2Identify distinct prime factors: Identify all the distinct prime factors from the prime factorization of the two 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 the prime factorization of either number. For 2, the highest power is 2^2 (which is from 12). For 3, the highest power is 3^1 (which is from 12).Find least common multiple (LCM): Multiply these highest powers of the distinct prime factors to find the least common multiple (LCM). Multiply 2^2 and 3 to find the LCM. 2^2 × 3 = 4 × 3 = 12 LCM of 12 and 2 is 12.

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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

12

and

2

\newline

\operatorname{lcm}(12,2)=

Identify prime factorization of $12$ : Identify the prime factorization of $12$ . $\newline$ Prime factorization of $12$ : $2 \times 2 \times 3$
Identify prime factorization of $2$ : Identify the prime factorization of $2$ . $\newline$ Prime factorization of $2$ : $2$
Identify distinct prime factors: Identify all the distinct prime factors from the prime factorization of the two 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 the prime factorization of either number. $\newline$ For $2$ , the highest power is $2^2$ (which is from $12$ ). $\newline$ For $3$ , the highest power is $3^1$ (which is from $12$ ).
Find least common multiple (LCM): Multiply these highest powers of the distinct prime factors to find the least common multiple (LCM). $\newline$ Multiply $2^2$ and $3$ to find the LCM. $\newline$ $2^2 \times 3 = 4 \times 3 = 12$ $\newline$ LCM of $12$ and $2$ is $12$ .