What is the least common multiple of 14 and 4 ? lcm(14,4)=

Identify prime factorization of 14: Identify the prime factorization of 14. Prime factorization of 14: 2 × 7Identify prime factorization of 4: Identify the prime factorization of 4. Prime factorization of 4: 2 × 2Identify distinct prime factors: Identify all the distinct prime factors from the prime factorizations of both numbers. 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). Multiply 2^2 (from 4) and 7 (from 14) to find the LCM. 2^2 × 7 = 4 × 7 = 28 LCM of 14 and 4 is 28.

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Math Problems

Grade 6

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 $28$ .