The HCF of two numbers is 8, and their LCM is 240. If the sum of the two numbers is 88, what are the numbers?
40 and 48
For two numbers a and b: \(a\times b = \text{HCF}\times\text{LCM} = 8\times240 = 1920\).
Also, \(a+b = 88\). Solving \(a+b=88\) and \(ab=1920\): the quadratic \(x^2-88x+1920=0\) factors as \((x-40)(x-48)=0\).
So the numbers are 40 and 48.
Hence, the two numbers are 40 and 48.
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Important Questions from LCM and HCF
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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?
