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Chapter 1: Q.946 (page 190)

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

60, 75

Short Answer

Expert verified

Least common multiple of 60, 75 is 300.

Step by step solution

01

Step 1. Given information. 

We have given numbers are 60, 75.

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:

List the first several multiples of each number.

Look for multiples common to both lists.

Look for the smallest number that is common to both lists.

This number is the LCM.

03

Step 3. Explanation. 

We have given numbers are 60 and 75.

Multiples of 60 are: 60, 120, 180, 240, 300, 360, 420, 480, 540, 600..

Multiples of 75 are: 75, 150, 225, 300, 375, 450, 525, 600, 675...

Common multiples between the multiples of 60 and 75 are 300 and 600 but we want least common multiple.

So the least common multiple of 60 and 75 is 300.

04

Step 4. Conclusion. 

Hence, the least common multiple of 60 and 75 is 300.

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