Two numbers are in ratio 14 : 9, if HCF and LCM of both numbers are 3 and 378, then find the greater number.
42
Since the numbers are in ratio 14 : 9 and these two integers have no common factor, the numbers can be written as \(14x\) and \(9x\), where \(x\) is their HCF.
Given the HCF is 3, so \(x = 3\), giving the numbers as \(14 \times 3 = 42\) and \(9 \times 3 = 27\).
Checking the LCM: \(\text{LCM} = 14 \times 9 \times 3 = 378\), which matches the given value.
Therefore, the greater number is 42.
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?
