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What is the least positive five-digit integer which when divided by 12 05 Aug 2021, 03:30
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66% (02:18) correct 34% (02:14) wrong based on 113 sessions

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What is the least positive five-digit integer which when divided by 12, 16, 21, 36 and 40 leave remainder 8 in each case?

(A) 10088
(B) 10080
(C) 10072
(D) 10048
(E) 10008
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What is the least positive five-digit integer which when divided by 12 05 Aug 2021, 04:09
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LCM of 12, 16, 21, 36 and 40 = 5040
Least integer value of a 5 digit number multiple of LCM of 12, 16, 21, 36 and 40 = 5040*2 =10080
least positive five-digit integer which when divided by 12, 16, 21, 36 and 40 leave remainder 8 in each case = 10080 + 8 = 10088

Option (A)

Bunuel
What is the least positive five-digit integer which when divided by 12, 16, 21, 36 and 40 leave remainder 8 in each case?

(A) 10088
(B) 10080
(C) 10072
(D) 10048
(E) 10008
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What is the least positive five-digit integer which when divided by 12 05 Aug 2021, 04:17
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Bunuel
What is the least positive five-digit integer which when divided by 12, 16, 21, 36 and 40 leave remainder 8 in each case?

(A) 10088
(B) 10080
(C) 10072
(D) 10048
(E) 10008
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The question basically means that we find the LCM of all the given numbers and add 8 to it.

LCM(12,16,21,36,40)=\(2^4*3^2*5*7=5040\). The number is 5040+8

The next number will be 2*5040+8=10088.


Options:
We can check each option, whether 8 less than it is multiple of the given numbers.

(A) 10088 ………10088-8=10080
0080 is divisible by 16, so 10080 is divisible by 16 or 2^4
1+0+08+0=9…..Thus divisible by 9.
10080=7*1440
Hence divisible by all.

(B) 10080………10080-8=10072……Not divisible by 5
(C) 10072 ………10072-8=10064……Not divisible by 5
(D) 10048 ………10048-8=10040……Not divisible by 3
(E) 10008 ………10008-8=10000……Not divisible by 3


A
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What is the least positive five-digit integer which when divided by 12 19 Jan 2025, 04:14
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Method 1: LCM Method

Since the number leaves the same remainder (8) when divided by 12, 16, 21, 36, 40
=> Number = Product of LCM(12,16,21,36,40) + 8

Attachment:
LCM.jpg
LCM.jpg [ 59.92 KiB | Viewed 785 times ]


Watch this video to MASTER LCM and GCD

=> Number = 5040k + 8 = 5040 * 2 + 8 = 10080 + 8 = 10088

Method 2: Divisibility Rules

Least positive five-digit integer which when divided by 12, 16, 21, 36 and 40 leave remainder 8

Subtract 8 from the answer choices and then lets check the answer choices

(A) 10088 - 8 = 10080
(B) 10080 - 8 = 10072
(C) 10072 - 8 = 10064
(D) 10048 - 8 = 10040
(E) 10008 - 8 = 10000

Now, above numbers should be divisible by 12, 16, 21, 36, 40

(A) 10,080
Sum of digits = 1 + 0 + 0 + 8 + 0= 9 => NOT Divisible by 3
Last two digits = 80 => Divisible by 4
=> Divisible by 12 => KEEP for now and check others

(B) 10,072
Sum of digits = 1 + 0 + 0 + 7 + 2= 10 => NOT Divisible by 3 => NOT divisible by 12 => ELIMINATE

(C) 10,064
Sum of digits = 1 + 0 + 0 + 6 + 4= 11 => NOT Divisible by 3 => NOT divisible by 12 => ELIMINATE

(D) 10,040
Sum of digits = 1 + 0 + 0 + 4 + 0= 5 => NOT Divisible by 3 => NOT divisible by 12 => ELIMINATE

(E) 10,000
Sum of digits = 1 + 0 + 0 + 0 + 0 = 1 => NOT Divisible by 3 => NOT divisible by 12 => ELIMINATE

So. Answer will be A
Hope it helps!

Watch the following video to MASTER Divisibility Rules

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