If the ratio of two numbers is \(8 : 3\), and their HCF is 8, then their LCM is:
192
Let the two numbers be \(8k\) and \(3k\), since their ratio is \(8:3\).
Since 8 and 3 are co-prime, the HCF of \(8k\) and \(3k\) is \(k\).
Given HCF \(= 8\), so \(k = 8\).
The numbers are \(8 \times 8 = 64\) and \(3 \times 8 = 24\).
For co-prime ratio parts, LCM \(= k \times 8 \times 3 = 8 \times 8 \times 3 = 192\).
Hence, the LCM of the two numbers is 192.
Similar Questions
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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?
