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 HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
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What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
