What is the least common multiple of 9 and 6 ? lcm(9,6)=

Identify prime factorization of 9: Identify the prime factorization of 9. Prime factorization of 9: 3 × 3Identify 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 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 the prime factor 2: The highest power is 2^1 (from 6). For the prime factor 3: The highest power is 3^2 (from 9).Find least common multiple (LCM): Multiply these highest powers together to find the least common multiple (LCM). Multiply 2^1 and 3^2 to find the LCM. 2^1 × 3^2 = 2 × 9 = 18 LCM of 9 and 6 is 18.

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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

9

and

6

\newline

\operatorname{lcm}(9,6)=

Identify prime factorization of $9$ : Identify the prime factorization of $9$ . $\newline$ Prime factorization of $9$ : $3 \times 3$
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 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 the prime factor $2$ : The highest power is $2^1$ (from $6$ ). $\newline$ For the prime factor $3$ : The highest power is $3^2$ (from $9$ ).
Find least common multiple (LCM): Multiply these highest powers together to find the least common multiple (LCM). $\newline$ Multiply $2^1$ and $3^2$ to find the LCM. $\newline$ $2^1 \times 3^2 = 2 \times 9 = 18$ $\newline$ LCM of $9$ and $6$ is $18$ .