Two numbers are in ratio 14 : 9, if HCF and LCM of both numbers are 3 and 378, then find the greater number.
42
Since the numbers are in ratio 14 : 9 and these two integers have no common factor, the numbers can be written as \(14x\) and \(9x\), where \(x\) is their HCF.
Given the HCF is 3, so \(x = 3\), giving the numbers as \(14 \times 3 = 42\) and \(9 \times 3 = 27\).
Checking the LCM: \(\text{LCM} = 14 \times 9 \times 3 = 378\), which matches the given value.
Therefore, the greater number is 42.
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?
