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Chapter 5: Problem 67

Find the least common multiple of the numbers. 240 and 285

Short Answer

Expert verified
The least common multiple of 240 and 285 is \(2^4 \times 3 \times 5 \times 19 = 6840\).

Step by step solution

01

Prime Factorization of the given numbers

Find the prime factorization of each number. For 240, it is \(2^4 \times 3 \times 5 \) and for 285, it is \(3 \times 5 \times 19\).
02

Identifying Common and Unique Factors

Identify common and unique factors between these factorizations. The common factors are 3 and 5, while the unique ones are \(2^4\) and 19.
03

Calculating the Least Common Multiple

Multiply all unique factors along with the highest power of common factors to obtain the LCM. So, the LCM of 240 and 285 is \(2^4 \times 3 \times 5 \times 19\).

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