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What is the least common multiple of 4 and 6 ?

lcm(4,6)=

What is the least common multiple of $4$ and $6$ ? $\newline$ $\operatorname{lcm}(4,6)=$

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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 $12$ .

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Question

For a given input value

u

g

outputs a value

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to satisfy the following equation.

\newline

-12 u+3=8 v+1

\newline

Write a formula for

g(u)

u

\newline

g(u)=

\newline

\square

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