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What is the least common multiple of 6 and 16 ?

lcm(6,16)=

What is the least common multiple of $6$ and $16$ ? $\newline$ $\operatorname{lcm}(6,16)=$

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Least common multiple of three or four numbers

Full solution

Q. What is the least common multiple of

6

and

16

?

\newline

\operatorname{lcm}(6,16)=

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 $16$ . Prime factorization of $16$ : $2^4$
Choose Highest Power: Identify all the distinct prime factors from the prime factorizations of the two numbers. $\newline$ Distinct prime factors: $2, 3$
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 is $2^4$ (from $16$ ). $\newline$ For $3$ , the highest power is $3^1$ (from $6$ ).
Find Least Common Multiple: Multiply these highest powers together to find the least common multiple (LCM). $\newline$ Multiply $2^4$ and $3$ to find the LCM. $\newline$ $2^4 \times 3 = 16 \times 3 = 48$ $\newline$ LCM of $6$ and $16$ is $48$ .

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