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What is the least common multiple of $12$ , $8$ , and $5$ ? $\newline$ $\_\_\_\_\_$

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Least common multiple of three or four numbers

Full solution

Q. What is the least common multiple of

12

,

8

, and

5

?

\newline

\_\_\_\_\_

Prime factorization of $12$ : Step $1$ : Prime factorization of $12$ . $\newline$ Prime factorization of $12$ : $2^2 \times 3$ .
Prime factorization of $8$ : Step $2$ : Prime factorization of $8$ . $\newline$ Prime factorization of $8$ : $2^3$ .
Prime factorization of $5$ : Step $3$ : Prime factorization of $5$ . $\newline$ Prime factorization of $5$ : $5$ .
Identify prime factors: Step $4$ : Identify all distinct prime factors from the factorizations. $\newline$ Distinct prime factors: $2$ , $3$ , $5$ .
Choose highest powers: Step $5$ : Choose the highest powers of all prime factors. $\newline$ Highest powers: $2^3$ , $3^1$ , $5^1$ .
Multiply highest powers: Step $6$ : Multiply the highest powers to find the LCM. $2^3 \times 3 \times 5 = 8 \times 3 \times 5 = 120$ .

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