The largest four-digit number which when divided by 6, 10 and 14 leaves remainder 3 in each case is:
9873
LCM of 6, 10 and 14: \(\text{LCM}(6,10,14) = 210\).
The required number is of the form \(210k+3\). For the largest 4-digit number: \(210k+3 \le 9999 \Rightarrow k \le 47.6\), so k=47.
\(210\times47+3 = 9870+3 = 9873\).
Hence, the largest four-digit number satisfying the condition is 9873.
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Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
