Concept
1) Find the L.C.M of all the given divisors.
2) subtract the difference between the divisor and the remainder from the L.C.M of all the divisors.
Calculation
L.C.M of 15, 25, 35 and 40 is 4200 (i.e. 5 × 3 × 5 × 7 × 8)
Difference of divisor and remainder = 15 - 10
⇒ 5
25 - 20
⇒ 5
35 - 30
⇒ 5
40 - 35
⇒ 5
Difference is 5 in each case
so, subtract 5 from 4200
4200 - 5
⇒ 4195
∴ The least number which when divided by 15, 25, 35, 40 leaves remainders 10, 20, 30, 35, respectively is 4195.
Shortcut Trick:
In such type of question,
Where Numbers a, b, c and Remainders x, y, z
Use format = LCM × k - D,
Where D = a - x = b -y = c - z
So, LCM of (15, 25, 35, 40) = 4200
K = 1
D = 5
Least number = 4200 - 5 = 4195
Answer
Hint: Here we will use the concept of the LCM. Firstly we will find the LCM of all the divisors i.e. 15, 25 and 35. Then we will see the pattern of getting the remainder by observing the difference between the divisor and the remainder. Then we will subtract the observed difference from the LCM of all the divisors to get the required value.
Complete step-by-step answer:
First, we will find the LCM of the divisors of the number i.e. 15, 25 and 35. Therefore, we get
So, option A is the correct option.
Note: Remainder is the value of the left over when a number is not exactly divisible by the other number. Zero is the remainder when a number exactly divides the other number.
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