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What is the least common multiple of $9$ , $3$ , and $4$ ? $\newline$ ____

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Least common multiple of three or four numbers

Full solution

Q. What is the least common multiple of

9

,

3

, and

4

?

\newline

____

Find Prime Factorization of $9$ : Find the prime factorization of $9$ . Prime factorization of $9$ : $3 \times 3$
Find Prime Factorization of $3$ : Find the prime factorization of $3$ . $\newline$ Prime factorization of $3$ : $3$
Find Prime Factorization of $4$ : Find the prime factorization of $4$ . $\newline$ Prime factorization of $4$ : $2 \times 2$
Identify Distinct Prime Factors: Identify all the distinct prime factors from the prime factorizations. $\newline$ Distinct prime factors: $2, 3$
Calculate LCM: Multiply the highest powers of all distinct prime factors to find the LCM. $\newline$ Multiply $2^2$ (from $4$ ) and $3^2$ (from $9$ ) to find the LCM. $\newline$ $2^2 \times 3^2 = 4 \times 9 = 36$

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