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
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?
