Find the smallest number which leaves remainder 5 15 and 20 when divided by 25,15 and 30 respectively
Answers
Given:
Divisors - 15, 25 & 30
Remainders - 5, 15 & 20
To find:
The smallest number which leaves remainder 5, 15 and 20 when divided by 15, 25 and 30 respectively
Solution:
1) We will subtract each of the given remainders from their respective divisors
15 - 5 = 10
25 - 15 = 10
30 - 20 = 10
∴ the difference in each case is 10
2) We will find the L.C.M of the divisors 15, 25 & 30
15 = 3 × 5
25 = 5 × 5
30 = 2 × 3 × 5
L.C.M. of 15, 25 & 30 = 2 × 3 × 5 × 5 = 150
3) Now, we will find the required smallest number which leaves remainder 5, 15 & 20 when divided by the divisors 15, 25 & 30 respectively.
∴ The smallest number = 150 - 10 = 140
Thus, 140 is the smallest number which leaves remainder 5 15 and 20 when divided by 25,15 and 30 respectively.
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