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
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?
