Question

Find the least multiple of 11 which when divided by 6 7 and 10 leaves the remainder 5 in each case

Answer 1

Answer:

Step-by-step explanation:

Let's say, x be the number which when divided by 6,9,15,18 leaves remainder 0. This implies (x+4) must leave remainder 4 when divided by the above numbers.The least number to satisfy the above condition is the LCM of the above numbers which is 90.

So, x=90. x+4=94

But 94 is not a multiple of 7.

With the help of hit and trial method,we can get

x=180,x+4=184 but not a multiple of 7.

x=270,x+4=274 but not a multiple of 7.

x=360,x+4=364.

364 leaves remainder 4 when divided by 6,9,15 and 18.And is also a multiple of 7.

Hence,364 is the least number satisfying all the conditions.