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What is the least common multiple of $14$ and $4$ ?

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Least common multiple

Full solution

Q. What is the least common multiple of

14

and

4

?

Identify prime factors: Identify the prime factors of $14$ . The prime factors of $14$ are $2$ and $7$ (since $14 = 2 \times 7$ ).
Identify prime factors: Identify the prime factors of $4$ . The prime factors of $4$ are $2$ and $2$ (since $4 = 2 \times 2$ ).
Determine LCM using prime factors: Determine the least common multiple (LCM) using the prime factors. $\newline$ To find the LCM, we take the highest powers of all prime factors that appear in either number. For $14$ , we have $2^1$ and $7^1$ . For $4$ , we have $2^2$ . The LCM will have $2^2$ (since it's the higher power of $2$ between the two numbers) and $7^1$ .
Calculate LCM: Calculate the LCM. $\newline$ LCM = $2^2 \times 7^1 = 4 \times 7 = 28$ .

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