What is the least common multiple of 8 and 10 ? lcm(8,10)=

Find Prime Factorization: To find the least common multiple (LCM) of 8 and 10, we first need to find the prime factorization of each number. The prime factorization of 8 is 2^3, since 8 = 2 * 2 * 2. The prime factorization of 10 is 2 * 5, since 10 = 2 * 5.Identify Highest Powers: Next, we identify the highest powers of all the prime factors that appear in the factorization of both numbers. For the number 8, the highest power of 2 is 2^3. For the number 10, the highest power of 2 is 2^1 and the highest power of 5 is 5^1.Calculate LCM: To find the LCM, we take the highest powers of all prime factors that appear in the factorization of both numbers. So, we take 2^3 from the number 8 and 5^1 from the number 10. Since there is no common factor of 5 in the prime factorization of 8, we only take the highest power of 5 from 10, which is 5^1.Multiply Highest Powers: Now, we multiply these highest powers together to get the LCM. LCM(8, 10) = 2^3 * 5^1 LCM(8, 10) = 8 * 5 LCM(8, 10) = 40

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What is the least common multiple of 8 and 10 ?

lcm(8,10)=

What is the least common multiple of $8$ and $10$ ? $\newline$ $\operatorname{lcm}(8,10)=$

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Q. What is the least common multiple of

8

and

10

\newline

\operatorname{lcm}(8,10)=

Find Prime Factorization: To find the least common multiple (LCM) of $8$ and $10$ , we first need to find the prime factorization of each number. $\newline$ The prime factorization of $8$ is $2^3$ , since $8 = 2 \times 2 \times 2$ . $\newline$ The prime factorization of $10$ is $2 \times 5$ , since $10 = 2 \times 5$ .
Identify Highest Powers: Next, we identify the highest powers of all the prime factors that appear in the factorization of both numbers. $\newline$ For the number $8$ , the highest power of $2$ is $2^3$ . $\newline$ For the number $10$ , the highest power of $2$ is $2^1$ and the highest power of $5$ is $5^1$ .
Calculate LCM: To find the LCM, we take the highest powers of all prime factors that appear in the factorization of both numbers. $\newline$ So, we take $2^3$ from the number $8$ and $5^1$ from the number $10$ . $\newline$ Since there is no common factor of $5$ in the prime factorization of $8$ , we only take the highest power of $5$ from $10$ , which is $5^1$ .
Multiply Highest Powers: Now, we multiply these highest powers together to get the LCM. $\newline$ LCM( $8$ , $10$ ) = $2^3 \times 5^1$ $\newline$ LCM( $8$ , $10$ ) = $8 \times 5$ $\newline$ LCM( $8$ , $10$ ) = $40$