The least number which when divided by 35, leaves a remainder of 25; when divided with 45 leaves a remainder of 35 and when divided by 55 leaves 45 as the remainder, is
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Answer:
The first number is divisor and the second number is its corresponding remainder.
35, 25
45, 35
55, 45
We are going to find the difference of these divisors and remainders corresponding to the divisors.
35−25=1045−35=1055−45=10
As you can see from the above that we are getting the same difference so to find the least number we have to take the L.C.M of 35, 45, 55 and then subtract 10 from the result of this L.C.M.
To find the L.C.M (35, 45, 55) we are going to write the factors of all the three numbers.
35=7×545=3×3×555=11×5
Now, the L.C.M of the three numbers will be the multiplication of the least number which is common among the three numbers.
L.C.M(35,45,55)=5×9×7×11⇒L.C.M(35,45,55)=3465
Subtracting 10 from the result of the L.C.M of the three numbers we get,
3465−10=3455
From the above solution, the least number which on division by 35 leaves a remainder 25 and on division by 45 leaves the remainder 35 and on division by 55 leaves the remainder 45 is 3455.