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What is the least common multiple of $8$ , $9$ , and $6$ ? $\newline$ ____

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Least common multiple of three or four numbers

Full solution

Q. What is the least common multiple of

8

,

9

, and

6

?

\newline

____

Prime Factorization of $8$ : Prime factorization of $8$ . Prime factorization of $8$ : $2^3$
Prime Factorization of $9$ : Prime factorization of $9$ . Prime factorization of $9$ : $3^2$
Prime Factorization of $6$ : Prime factorization of $6$ . Prime factorization of $6$ : $2 \times 3$
Identify Prime Factors: Identify all distinct prime factors from the factorizations. $\newline$ Distinct prime factors: $2, 3$
Choose Highest Powers: Choose the highest powers of all prime factors. $\newline$ Highest powers: $2^3$ , $3^2$
Multiply to Find LCM: Multiply the highest powers to find the LCM. $\newline$ $2^3 \times 3^2 = 8 \times 9 = 72$

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