Question

find the greatest 3 digit number which when divided by 75,45,60 leaves no remainder the remainder 4in each case

Answer 1

From the given condition, we have to rearrange the numbers as 75=3×52, 45=32×5 and 60=22×3×5.

It is significant to find the LCM of these given numbers including 75, 45, 60. It is further expanded as 5^2×3^2×2^2=25×9×4. And, we finally get the value as 900.

The next number divisible by the three numbers is 1800, but it is a 4 digit number. Hence, the answer to this question is 900.

Answer 2

Answer:

i)900 ii)908

Step-by-step explanation:

i) leaves no remainder:

for this first we have to find LCM(75,45,60)

75= 3×5×5=3×5²

45= 3×3×5=3²×5

60= 2×2×3×5=2²×3×5

∴ LCM = 2²×3²×5² =900

(∵ 900 is 3 digit number)

ii) leaves the remainder 4 :

for this we have to add 4 to lcm(75,45,60)

i.e., 4+900=904

verification: divide 908 with 75,45 and 60 we get remainder as 4.

        45)904(20

             900                        ∴remainder is 4

               4