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Chapter 5: Problem 64

Find the least common multiple of the numbers. 220 and 400

Short Answer

Expert verified
The least common multiple of 220 and 400 is 4400.

Step by step solution

01

Prime Factorization

First, we perform the prime factorization of each number: - The prime factors of \(220 = 2^2 \times 5^1 \times 11^1\)- The prime factors of \(400 = 2^4 \times 5^2\)
02

Identification of Unique Prime Factors

Next, we identify the unique prime factors of the two numbers: \(2, 5,\) and \(11\). We ignore any repeated factors.
03

Multiply Each Factor the Greatest Number of Times it Occurs

Now, we multiply each unique prime factor by the greatest number of times it appears in either breakdown: - \(2\) appears \(4\) times,- \(5\) appears \(2\) times and - \(11\) appears \(1\) time.So the LCM is \(2^4 \times 5^2 \times 11^1\)
04

Calculate the LCM

Finally, we calculate the value of the LCM by multiplying the factors together: \(2^4 = 16\), \(5^2 = 25\) and \(11 = 11\). Therefore, \(16 \times 25 \times 11 = 4400\).

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