Question

Find the least number, greater that 10000, which when divided by 5, 10, 12, 15, 18, 25 and 30 leaves the remainder 2 in each case. Find the greatest number of four digits which when divided by 5, 10, 12, 15, 18, 25 and 30 leaves the​

Answer 1

Step-by-step explanation:

first we need to find least common multiple of 5, 10, 12, 15, 18, 25 and 30.

we can solve as l.c.m (5, 10, 15, 25,30) = 150 and l.c.m (12, 18) = 36, now to find l.c.m( 5, 10, 15, 12, 18, 25, 30 ) = l.c.m (150, 36) = 900. so any number which gives us remainder 3 must be in the form of N= 900 k+3 for some k integer.

so k= 1, N= 903 which is three digit number.

for k=2, N=1803 which is four digit number.

continuing in this manner we have

for k= 11, N= 9903 which is four digit number.

for k=12, N= 10803 which is five digit number.

so the least five digit number which gives remainder 3 when divided by 5, 10, 12, 15, 18, 25 and 30 is 10803.

thanks

Answer 2

Answer:

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Step-by-step explanation: