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Chapter 1: Problem 7

For the following problems, find the least common multiple of given numbers. 24,36

Short Answer

Expert verified
Answer: The least common multiple (LCM) of 24 and 36 is 72.

Step by step solution

01

Find prime factors of each number

To begin, list the prime factors of each number: 24: 2 脳 2 脳 2 脳 3 (2^3 脳 3) 36: 2 脳 2 脳 3 脳 3 (2^2 脳 3^2)
02

Identify the highest power of each unique factor

Now that we have the prime factors of each number, we need to determine the highest power of each unique factor. In this case, our unique factors are 2 and 3. For the factor 2, the highest power between 24 and 36 is 2^3. For the factor 3, the highest power between 24 and 36 is 3^2.
03

Multiply the highest powers of each unique factor

To calculate the LCM, multiply the highest powers of each unique factor: LCM = 2^3 脳 3^2 = 8 脳 9 = 72
04

State the answer

The least common multiple (LCM) of 24 and 36 is 72.

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