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
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
