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Chapter 1: Q.947 (page 190)

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

24, 30

Short Answer

Expert verified

Least common multiple of 24, 30 is 120.

Step by step solution

01

Step 1. Given information. 

We have given numbers are 24, 30.

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 24 and 30.

Prime factors of 24 are: 2 x 2 x 2 x 3

Prime factorization of 30 are: 2 x 3 x 5

Multiply each factor the greatest number of times it occurs in either 24 or 30.

So LCM = 2 x 2 x 2 x 3 x 5 = 120

04

Step 4. Conclusion. 

Hence, least common multiple of 24, 30 is 120.

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