The ratio of sum to the LCM of two natural numbers is 12:35. If their HCF is 6, then the smaller num

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20 May 2022 LCM & HCF

The ratio of sum to the LCM of two natural numbers is 12:35. If their HCF is 6, then the smaller number is

OPtion

1) 24
2) 42
3) 54
4) 30
5) 48
6) 12
7) 36
8) 18
9) 60
10) None of these

Solution

Let the numbers be 6x and 6y where x and y are prime to each other.
Then, LCM = 6xy
(6x + 6y) / 6xy = 12/35
35(x+y) = 12xy
⇒ x=5, y=7
Smallest number=6x=6*5=30
Correct Option 4)

Correct Option: 4 Best Solution (0)