Three numbers are in the ratio 3 : 7 : 2, and their LCM is 5376. Their HCF is:
128
Since 3, 7 and 2 are pairwise coprime, the LCM of the ratio terms is \(3\times7\times2=42\).
If the numbers are 3k, 7k and 2k, their LCM is \(42k\).
Setting \(42k=5376\) gives \(k=128\), which is also the HCF since the ratio terms are coprime.
Hence, the HCF of the three numbers is 128.
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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?
