What is the least common multiple of 4 and 6 ? lcm(4,6)=

Identify prime factorization of 4: Identify the prime factorization of 4. Prime factorization of 4: 2 × 2Identify prime factorization of 6: Identify the prime factorization of 6. Prime factorization of 6: 2 × 3Identify distinct prime factors: Identify all the distinct prime factors from the prime factorizations of the two numbers. Distinct prime factors: 2, 3Choose highest powers of distinct prime factors: 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 (from 4). For 3, the highest power is 3^1 (from 6).Multiply highest powers to find LCM: Multiply these highest powers together to find the least common multiple (LCM). Multiply 2^2 and 3^1 to find the LCM. 2^2 × 3^1 = 4 × 3 = 12 LCM of 4 and 6 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

4

and

6

\newline

\operatorname{lcm}(4,6)=

Identify prime factorization of $4$ : Identify the prime factorization of $4$ . $\newline$ Prime factorization of $4$ : $2 \times 2$
Identify prime factorization of $6$ : Identify the prime factorization of $6$ . $\newline$ Prime factorization of $6$ : $2 \times 3$
Identify distinct prime factors: Identify all the distinct prime factors from the prime factorizations of the two numbers. $\newline$ Distinct prime factors: $2$ , $3$
Choose highest powers of distinct prime factors: 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 $2^2$ (from $4$ ). $\newline$ For $3$ , the highest power is $3^1$ (from $6$ ).
Multiply highest powers to find LCM: Multiply these highest powers together to find the least common multiple (LCM). $\newline$ Multiply $2^2$ and $3^1$ to find the LCM. $\newline$ $2^2 \times 3^1 = 4 \times 3 = 12$ $\newline$ LCM of $4$ and $6$ is $12$ .