What is the least common multiple of 6 and 10 ? lcm(6,10)=

Identify Prime Factorization: Identify the prime factorization of 6. Prime factorization of 6: 2 × 3Find Distinct Prime Factors: Identify the prime factorization of 10. Prime factorization of 10: 2 × 5Choose Highest Power: Identify all the distinct prime factors from the prime factorization of the two numbers. Distinct prime factors: 2, 3, 5Multiply Highest Powers: 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 in the factorizations is 2^1 (as it appears in both 6 and 10). For 3: The highest power in the factorizations is 3^1 (as it appears in 6). For 5: The highest power in the factorizations is 5^1 (as it appears in 10).Find Least Common Multiple: Multiply these highest powers together to find the least common multiple (LCM). Multiply 2^1, 3^1, and 5^1 to find the LCM. 2 × 3 × 5 = 30 LCM of 6 and 10 is 30.

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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

6

and

10

\newline

\operatorname{lcm}(6,10)=

Identify Prime Factorization: Identify the prime factorization of $6$ . Prime factorization of $6$ : $2 \times 3$
Find Distinct Prime Factors: Identify the prime factorization of $10$ . Prime factorization of $10$ : $2 \times 5$
Choose Highest Power: Identify all the distinct prime factors from the prime factorization of the two numbers. $\newline$ Distinct prime factors: $2$ , $3$ , $5$
Multiply Highest Powers: 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 in the factorizations is $2^1$ (as it appears in both $6$ and $10$ ). $\newline$ For $3$ : The highest power in the factorizations is $3^1$ (as it appears in $6$ ). $\newline$ For $5$ : The highest power in the factorizations is $5^1$ (as it appears in $10$ ).
Find Least Common Multiple: Multiply these highest powers together to find the least common multiple (LCM). $\newline$ Multiply $2^1$ , $3^1$ , and $5^1$ to find the LCM. $\newline$ $2 \times 3 \times 5 = 30$ $\newline$ LCM of $6$ and $10$ is $30$ .