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 HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
