Chapter 1: Q.15 (page 21)

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.
28, 40

Short Answer

Expert verified

The least common multiple of 28 and 40 is 280.

Step by step solution

Step 1. Given information

The given numbers are 28 and 40.

The least common multiple of the given numbers is to be determined using prime factors.

Step 2. Calculating the prime factors

For prime factorization, the given number is to be factored such that all the factors are prime numbers.

$28 = 2 \cdot 14 28 = 2 \cdot 2 \cdot 7$

The factors are all primes here and cannot be further factored.

$40 = 2 \cdot 20 40 = 2 \cdot 2 \cdot 10 40 = 2 \cdot 2 \cdot 2 \cdot 5$

The factors are all primes here and cannot be further factored.

Step 3. Calculating least common multiple

To determine LCM, the prime factors of both the numbers are to be considered and the factors that are present in both are to be taken whereas the repeated factors are to be taken only once.

$LCM = 2 \cdot 2 \cdot 2 \cdot 5 \cdot 7 LCM = 280$

Step 4. Conclusion

Therefore, the least common multiple of 28 and 40 is 280.

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In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.
28, 40

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the prime factors

Step 3. Calculating least common multiple

Step 4. Conclusion

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In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.28, 40

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the prime factors

Step 3. Calculating least common multiple

Step 4. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Logic and Functions

Applied Mathematics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.
28, 40