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The greatest number of four digits which is divisible by 15, 25, 40 and 75 is: _____   Greatest number of 4-digits is 9999. To find the LCM of 15, 25, 40 and 75. 15 = 3 × 5 25 = 5 × 5 40 = 2 × 2 × 2 × 5 75 = 3 × 5 × 5 L.C.M. of 15, 25, 40 and 75 = 2 × 2 × 2 × 3 × 5 × 5 = 600. On dividing 9999 by 600, the remainder is 399. Required number (9999 - 399) = 9600.     PLEASE GO THROUGH THE ABOVE SOLUTION AND EXPLAIN ME THE FOLLOWING POINTS :   Why we took LCM OF 15 , 25 , 40 , 75(REASON IN BREIF ) WHY WE DIVIDED THE LCM (600) AND 9999. WHY WE SUBTRACTED THE REMAINDER WHY SUBTRACTING THE REMAINDER GIVES US THE ANSWER. HOPE YOU EXPLAIN IN BREIF REGARDS, ANAS
Asked by anasfaisal123456 | 26 Mar, 2020, 06:53: PM Expert Answer
The LCM is considered since it is the multiple of all the four numbers given and hence divisible by them and we are required to find the number divisible by all of these numbers.
As the required number should be a 4-digit number as well as divisible by the given 4 numbers. So, if a number is divisible by hte LCM of the numbers, then it will be divisible by those four numbers (15, 25, 40 and 75)
Subtracting the remainder from a number gives the multiple of LCM and so the subtraction of remainder happens.
As the required number is the greatest 4 digits number divisible by the given numbers, so the number obtained after subtracting the remainder is the required number.
Answered by Renu Varma | 27 Mar, 2020, 11:21: AM

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