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Chapter 1: Q.948 (page 190)

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

70, 84

Short Answer

Expert verified

Lest common multiple of 70, 84 is 420.

Step by step solution

01

Step 1. Given information.  

We have given numbers are 70, 84.

02

Step 2. Concept used. 

Least Common Multiple: The smallest positive number that is a multiple of two or more numbers.

Steps to find the least common multiple using prime factorization:

Find the prime factorization of each number.

Write each number as a product of primes, matching primes vertically when possible.

Bring down the primes in each column.

Multiply the factors to get the LCM.

03

Step 3. Explanation.  

We have given numbers are 70 and 84.

Prime factors of 70 are: 2 x 5 x 7

Prime factors of 84 are: 2 x 2 x 3 x 7

Multiply each factor the greatest number of times it occurs in either 70 or 84.

So LCM = 2 x 2 x 3 x 5 x 7 = 420

04

Step 4. Conclusion. 

Hence, lest common multiple of 70, 84 is 420.

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