Question

The sum and different of lcm and hcf of two numbers are 592and518

Answer 1

Answer:

74

Step-by-step explanation:

Let the L.C.M and H.C.F be x and y respectively.  

x + y = 592  

x - y = 518  

x = 555 & y = 37  

Now let the numbers be 37a and 37b  

37a +37b = 296  

a + b = 8  

Possible pairs of co-primes, whose sum is 8 are (1, 7) & (3, 5)  

Possible pair of numbers are (37×1, 37×7) = (37, 259)  

and (37×3, 37×5) = (111, 185)  

Now H.C.F × L.C.M. = 555 × 37 = 20535  

Also 111 × 185 = 20535, while 37 × 259 ≠ 20535  

Hence the required numbers are 111 and 185