The largest four-digit number which when divided by 14, 15 and 8 leaves remainder 4 in each case is:
9244
A number leaving remainder 4 when divided by 14, 15 and 8 must be 4 more than a common multiple of these numbers.
\(\text{LCM}(14,15,8) = 840\).
The largest 4-digit multiple of 840 is \(840\times11 = 9240\), since \(840\times12=10080\) exceeds 9999.
Adding the remainder: \(9240+4 = 9244\).
Hence, the required number is 9244.
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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:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
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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?
