# Find the Smallest Number Which When Increased by 17 is Exactly Divisible by 520 and 468

By BYJU'S Exam Prep

Updated on: September 25th, 2023

4663 is the smallest number which when increased by 17 is exactly divisible by 520 and 468. By determining the least common multiple (LCM) of 520 and 468 and subtracting 17 from it, we can identify the smallest number that fulfills this condition. So, scroll on and learn step-by-step how 4663 is the smallest number that, when increased by 17, is divisible by both 520 and 468.

## What is LCM?

Finding the smallest common multiple between any two or more numbers is done using the least common multiple (LCM) approach. A number that is a multiple of two or more other numbers is said to be a common multiple. Finding the LCM is useful in various mathematical operations, such as adding or subtracting fractions, simplifying ratios, and solving equations.

### How to find LCM?

The smallest common multiple for any two or more given numbers is the least common multiple, as we have already established.

A multiple is the result of multiplying two numbers together. In the same way that 4 is a multiple of 2, we get 4 when we multiply 2 by 2. Similar to the math table, you can see a number’s multiples when you multiply it by 1, 2, 3, 4, 5, 6, and so on, but not by zero.

## Smallest Number Divisible by 520 and 468 When Increased by 17

To find the smallest number that, when increased by 17, is divisible by both 520 and 468, we need to find their least common multiple (LCM).

Step 1: Determine the LCM

468 and 520 are the given numbers

Prime factors of 468 are

468 = 2 x 2 x 3 x 3 x 13

Prime factors of 520 are

520 = 2 x 2 x 2 x 5 x 13

LCM of 468 and 520 is

LCM (468, 520) = 2 x 2 x 2 x 3 x 3 x 13 x 5 = 4680

Step 2: Calculate the smallest number

The integer multiplied by 17 is precisely divisible by 520 and 468 under the conditions stated.

4680 – 17 = 4663

Summary:

## Find the Smallest Number Which When Increased by 17 is Exactly Divisible by 520 and 468

4663 is the smallest number which is exactly divisible by 520 and 468 after it is increased by 17. Least Common Multiple (LCM) is a method to determine the smallest common multiple of any two or more numbers.

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