Question

find the greatest 3 digit number which when divided by 35 ,40 and 60 leaves the remainder 3 in each case​

Answer 1

Answer:

greatest 3 digit number = 843

Step-by-step explanation:

Answer 2

The greatest 3 digit number which when divided by 35 ,40 and 60 leaves the remainder 3 in each case​ is 843

Solution:

First we will calculate LCM of 35 , 40 and 60

Calculate the prime factors of 35 and 40 and 60

$35 = 5 \times 7\\\\ 40 = 2^3 \times 5\\\\60 = 2^2 \times 3 \times 5$

Now multiply the factors which are common in 35 and 40 and 60 that has highest power

$LCM = 2^3 \times 3 \times 5 \times 7 = 840$

L.C.M (35,40,60)  = 840

As you Know, the greatest 3 digit number is 999

When we divide 999 with 840, we get 159 as the remainder and 1 as the quotient

Now, when we subtract the remainder from the dividend we get 840, which is the greatest 3 digit number completely divisible by 35, 40 and 60

Hence the greatest 3 digit number which will give 3 as a remainder on dividing by 35, 40 and 60 remainder will be = (840 + 3) = 843

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