What is the least six-digits positive integer which is perfectly divis

Question

What is the least six-digits positive integer which is perfectly divisible by 12, 25, 45 and 60?

(A) 100,800 
(B) 201,600 
(C) 302,400
(D) 400,800 
(E) 500,400

Nidzo · Answer

Looking at the numbers 12, 25, 45 and 60 the answer must meet the divisibility rules for 3 (sum of digits is divisible by 3), 4 (last two digits are divisible by 4) and 5 (numbers will end in 0 or 5).

As all answer choices meet the divisibility rules for 3, 4 and 5, I would say that the Answer is A.

As all answer choices meet the divisibility rules for  3 ,  4  and  5 , I would say that the Answer is A.

PrachiMaloo · Answer

Can anyone explain this question?

Fdambro294 · Answer

The question is effectively asking for the first 6 Digit Multiple of the Lowest Common Multiple into which each of the Integers must Divide Evenly

12 = (2)^2 (3)

25 = (5)^2

45 = (3)^2 (5)

60 = (2)^2 (3) (5)

LCM = (2)^2 (3)^2 (5)^2 = (4) (9) (25) = 900

Effectively, we are looking for an answer choice that is Divisible by this LCM of 900

Factor Foundation Rule: in order for a number to be divisible by 900, that number must be divisible by all the Factors that make up that number

900 = (100) (9)

Thus, we are looking for the answer choice that is divisible by BOTH 100 and 9 ———> in such a case the number will be divisible by 900

Rule: to be divisible by 100, an integer must contain at least 2 Trailing Zeros

Rule: to be Divisible by 9, the SUM of the Digits of that number must be divisible by 9

(A) 100, 800

Meets both conditions and is the least value

Answer A

Without looking at the answer choices, you could logically put this answer together.

We need the lowest 6 digit integer…..

6 digit integers start with ——-> 100,000

That is divisible by 900: in other words, that is divisible by BOTH 100 and 9

the last 2 digits must be 0

So far, we still have 100,000 but we need to make this divisible by 9 while Minimizing how high we make the value

The current sum of digits = 1

If we change one of the 0 digits to an 8, we will get a Sum of Digits = 9 ———> and the number will be divisible by 9

But we need to keep the last 2 digits 0 in order for 100 to divide the number evenly.

Placing the 8 digit in the 100s Place will minimize the value

100,800

Posted from my mobile device

What is the least six-digits positive integer which is perfectly divis

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

What is the least six-digits positive integer which is perfectly divis

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards