What Is The Smallest Five Digit Number That Is Divisible by 16, 24, 36 and 54? GMAT Problem Solving

Question: What is the smallest five digit number that is divisible by 16, 24, 36 and 54?

1. 10320
2. 10080
3. 10032
4. 10368
5. None of the above

‘What is the smallest five digit number that is divisible by 16, 24, 36 and 54?’ - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide 2022”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

This question can be solved by only one approach.
It is asked in the question to find out the smallest five-digit number that is divisible by 16, 24, 36, and 54.
The number must be divisible by all the factors.
Let us break these factors of the five-digit number into primes.
16 = 2*2*2*2
The LCM must have 2^4 in it.
24 = 2 * 2 *2 *3
As the LCM has 4 2’s it should also have a 3 in it
36 = 4*9 = 2 * 2 * 3 * 3
As we already have one 3 in the LCM we need to add one more 3.
Our LCM = 2*2*2*2 *3*3
Now the last number is 54
54 = 2*27 = 2*3*3*3
We already have lots of two’s in the LCM we need only one 3 to make 54 also a factor of the number
LCM = 2*2*2*2*3*3*3
In the question, it was asked to find the minimum 5 digit number that has factors 16, 24, 36, 54
The LCM = 2^4 * 3^3 = 16 * 27 = 432
Now the given number must be the multiple of 432.
The smallest five-digit number is 10000
Dividing it by 432
10000/432 = 23.14
Now let us consider two numbers 23 and 24
432 * 23 = 9936 (this is a 4 digit number and hence not sufficient)
432 * 24 = 10368 (this is a 5-digit number)
The smallest 5 digit number having factors 16, 24, 36, 54 is 10368, hence option D is the correct answer.

Correct Answer: D

Suggested GMAT Problem Solving Questions

• The Population of the Bacteria Colony Doubles Every Day GMAT Problem Solving
• If tu=xytu=xyand ty=uxty=ux Where t, u, x, and y are Non-Zero Integers GMAT Problem Solving 
• A Farm has Chickens, Cows and Sheep GMAT Problem Solving 
• In how Many Different Ways Can a Group of 8 People be Divided into 4 Teams of 2 People Each? GMAT Problem Solving 
• If 4 People are Selected from a Group of 6 Married Couples GMAT Problem Solving 
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving
• A Conference Room is Equipped with a Total of 45 Metal or Wooden Chairs.GMAT Problem Solving 
• A Welder Received an Order to Make a 1 Million Litre Cube-Shaped Tank. GMAT Problem Solving 
• Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours. GMAT Problem Solving 
• What is the Value of k if the Sum of Consecutive Odd Integers From 1 to k Equals 441? GMAT Problem Solving 
• A Circle with a Radius R is Inscribed into a Square with a Side K. GMAT Problem Solving 
• Machine A can do a Certain Job in 12 Days Working 2 Full Shifts GMAT Problem Solving 
• The square of 5√252 =? GMAT Problem Solving 
• After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving 
• If 12 Ounces of a Strong Vinegar Solution are Diluted with 50 Ounces GMAT Problem Solving 
• A Contractor Estimated that his 10-Man Crew GMAT Problem Solving 
• A Circle is Inscribed in a Square with the Diagonal of 4 Centimeters.  GMAT Problem Solving 
• At a Dog Competition, a Dog is Awarded 10 Points if it Runs GMAT Problem Solving