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

By K Balaji|Updated : November 7th, 2022

4663 is the smallest number which when increased by 17 is exactly divisible by 520 and 468.

Step 1: To get the solution we have to 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

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.

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.

Summary:-

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

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

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