Three numbers are in the ratio \(3:7:2\), and their LCM is 8820. Their HCF is:
210
Since the ratio is \(3:7:2\) and these coefficients share no common factor, let the numbers be \(3k, 7k, 2k\), where \(k\) is their HCF.
The LCM of \(3k, 7k, 2k\) equals \(k \times \text{LCM}(3,7,2) = k \times 42 = 42k\).
Given \(42k = 8820\), so \(k = \frac{8820}{42} = 210\).
The HCF is \(k = 210\).
Hence, the HCF of the three numbers is 210.
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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?
