College

We appreciate your visit to Use any method to find the least common multiple of the numbers 21 49 and 147 The least common multiple of 21 49 and 147. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Use any method to find the least common multiple of the numbers 21, 49, and 147.

The least common multiple of 21, 49, and 147 is __________. (Simplify your answer.)

Answer :

To find the least common multiple (LCM) of the numbers 21, 49, and 147, we can use the prime factorization method. Here's a step-by-step explanation:

1. Prime Factorize Each Number:

- 21: The prime factors of 21 are [tex]\(3\)[/tex] and [tex]\(7\)[/tex] because [tex]\(21 = 3 \times 7\)[/tex].

- 49: The prime factors of 49 are [tex]\(7\)[/tex] and [tex]\(7\)[/tex] (or [tex]\(7^2\)[/tex]) because [tex]\(49 = 7 \times 7\)[/tex].

- 147: The prime factors of 147 are [tex]\(3\)[/tex] and [tex]\(7\)[/tex] (or [tex]\(7^2\)[/tex]) because [tex]\(147 = 3 \times 7 \times 7\)[/tex].

2. Identify the Highest Power of Each Prime Factor:

- For the prime factor [tex]\(3\)[/tex], the highest power appearing in the factorizations is [tex]\(3^1\)[/tex].

- For the prime factor [tex]\(7\)[/tex], the highest power appearing is [tex]\(7^2\)[/tex].

3. Multiply the Highest Powers Together:

To find the LCM, we multiply the highest power of each prime factor together:

[tex]\[
\text{LCM} = 3^1 \times 7^2 = 3 \times 49 = 147
\][/tex]

So, the least common multiple of 21, 49, and 147 is 147.

Thanks for taking the time to read Use any method to find the least common multiple of the numbers 21 49 and 147 The least common multiple of 21 49 and 147. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada