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What is the least common multiple of 14 and 4 ?

lcm(14,4)=

What is the least common multiple of $14$ and $4$ ? $\newline$ $\operatorname{lcm}(14,4)=$

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Least common multiple of three or four numbers

Full solution

Q. What is the least common multiple of

14

and

4

?

\newline

\operatorname{lcm}(14,4)=

Identify prime factorization of $14$ : Identify the prime factorization of $14$ . $\newline$ Prime factorization of $14$ : $2 \times 7$
Identify prime factorization of $4$ : Identify 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 of both numbers. $\newline$ Distinct prime factors: $2, 7$ (Note that $2$ is already included, so we only count it once, but we need to account for the highest power of $2$ present in either number, which is $2^2$ from the number $4$ ).
Find least common multiple (LCM): Multiply the distinct prime factors, using the highest powers found in either number, to find the least common multiple (LCM). $\newline$ Multiply $2^2$ (from $4$ ) and $7$ (from $14$ ) to find the LCM. $\newline$ $2^2 \times 7 = 4 \times 7 = 28$ $\newline$ LCM of $14$ and $4$ is $28$ .

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