Question

Find the least five digit number which dividing by 4,12,20,24 leaves a remainfer 3 in each case

Answer 1

LCM OF 4, 12, 20, 24

4 = 2 X 2
12 = 2 X 2 X 3
20 = 2 X 2 X 5
24 = 2 X 2 X 2 X 3

LCM = 2 X 2 X 3 X 5 X 2
LCM = 120

NOW, WE WILL FIND THE MULTIPLE OF 120 THAT IS EXACTLY OF 5 DIGITS AND ALSO LEAST IN THAT MULTIPLE.

IF WE MULTIPLY 84 INTO 120 THEN WE WILL FIND 10080 THAT IS THE LEAST MULTIPLE OF 120 THAT IS OF 5 DIGITS.


QUESTIONS SAYS THAT THE REMAINDERS SHOULD BE 3 IN EACH CASE.

SO,

ADDING 3 IN THE 84TH MULTIPLE OF 120. 84TH MULTIPLE OF 120

10080 + 3 = 10083

SO,

10083 IS THE LEAST NUMBER OF FIVE DIGITS THAT CAN DIVISIBLE BY 4, 12, 20, 24 AND LEAVING 3 AS A REMAINDER IN EACH CASE.

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