Chapter 1: Q.16 (page 21)

In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.
84, 90

Short Answer

Expert verified

The least common multiple of 84 and 90 is 1260.

Step by step solution

Step 1. Given information

The given numbers are 84 and 90.

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.

$84 = 2 \cdot 42 84 = 2 \cdot 2 \cdot 21 84 = 2 \cdot 2 \cdot 3 \cdot 7$

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

$90 = 2 \cdot 45 90 = 2 \cdot 3 \cdot 15 90 = 2 \cdot 3 \cdot 3 \cdot 5$

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.

$LCM = 2 \cdot 2 \cdot 3 \cdot 3 \cdot 5 \cdot 7 LCM = 1260$

Step 4. Conclusion

Therefore, the least common multiple of 84 and 90 is 1260.

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In the following exercises, find the least common multiple of each pair of numbers using the prime factors method.
84, 90

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.84, 90

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

Calculus

Probability and Statistics

Geometry

Statistics

Theoretical and Mathematical Physics

Mechanics Maths

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.
84, 90