The LCM of two numbers is 7 times their HCF. The sum of LCM and HCF is 240. find
the two numbers.
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The LCM of two numbers is 7 times their HCF. The sum of LCM and HCF is 240. find
the two numbers.
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Given info : The LCM of two numbers is 7 times their HCF and the sum of LCM and HCF is 240.
To find : The two numbers are ..
solution : let HCF of two numbers is m.
we know, HCF of numbers is highest common factor among them.
so we can assume , two numbers ma and mb where a and b are co - prime numbers.
using formula,
HCF × LCM = product of numbers
⇒ m × 7m = ma × mb
[ as LCM is 7 times of their HCF. ]
⇒7 = ab
now we can assume a = 1 , b = 7 [ because a and b are co - prime numbers ]
again, sum of HCF and LCM = 240
⇒m + 7m = 240
⇒m = 30
now numbers are ; ma = 30 × 1 = 30 and mb = 30 × 7 = 210
Therefore the numbers are 30 and 210