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# Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**The greatest number of 6 digits exactly divisible by 24, 15, and 36 is 999720**. To find the greatest number of six digits divisible by 24, 15, and 36, we need to identify the least common multiple (LCM) of these three numbers. The LCM is the smallest multiple that is evenly divisible by all the given numbers. By determining the LCM, we can ensure that the desired number will be divisible by each of the given numbers individually.

In this article, we have explained the step-by-step process of finding the greatest six-digit number that satisfies the given divisibility conditions.

Table of content

## Greatest 6 digits Number divisible by 24, 15 and 36

Let’s start by finding the LCM of 24, 15, and 36. We can break down each number into its prime factors:

Multiple of 24 = 2 x 2 x 2 x 3

Multiple of 15 = 3 x 5

Multiple of 36 = 2 x 2 x 3 x 3 = 22 x 32

Now, we take the highest power of each prime factor that appears in any of the given numbers. In this case, we have 2^{3}, 3^{2}, and 5. Multiplying these prime factors together, we get the LCM:

LCM of 24, 15, 36 = 23 x 32 x 5 = 360

Afterward, multiply the largest 6-digit number by 360.

999999/360 = 2777.775 with the remainder 279

Now, 999999 – 279 = 999720

999720 is the largest six-digit number that can be divided into 24, 15, and 36.

## Types of Numbers

Numbers can be divided into sets called number systems. The different kinds of numbers in Mathematics are:

**Natural Numbers**: Natural numbers are known as counted numbers and include positive integers from 1 to infinity.**Integers**: Integers are called non-negative integers and do not contain fractions or decimals.**Integers**: Integers are the set of all integers, including the negative set of natural numbers.**Real Numbers**: All positive and negative integers, fractions, and decimals that do not contain imaginary numbers are called real numbers.**Rational Numbers**: Any number that can be written as the ratio of one number to another number is written as a rational number.**Irrational Numbers**: Numbers that cannot be represented in relation to each other are called irrational numbers and are denoted by the symbol “P”.**Complex Numbers**: A number that can be written in the form a+bi, where “a and b” are real numbers and “i” is an imaginary number, is called a complex number “C”.**Imaginary Numbers**: Imaginary numbers are complex numbers that can be written in the form of the product of a real number and the imaginary unit “i”.

**Summary**:

## Find the greatest number of 6 digits exactly divisible by 24, 15 and 36.

**The greatest six-digit number that is exactly divisible by 24, 15, and 36 is 999,720.** We determined this by finding the least common multiple (LCM) of the given numbers and subtracting the remainder from the largest six-digit number. Numbers are fundamental to representing quantities and performing calculations. In this case, we utilized arithmetic principles and the concept of LCM to identify the largest sum of six numbers that meet the divisibility criteria of 24, 15, and 36, resulting in a value of 999,720.

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