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
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
