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Given:
We need to find the least number which when divided by 20, 25, 35 and 40 leaves remainders 14, 19, 29 and 34 respectively.
Concept used:
If difference between the given number and remainder remains same for each number, the required number will be the (LCM of the divisors - the constant difference)
Calculations:
Let us see the relation between the pairs of numbers if there is any:
20 - 14 = 6
25 -19 = 6
35 - 29 = 6
40 - 34 = 6.
The difference is 6
Now, the LCM of 20, 25, 35 and 40.
20 = 2 × 2 × 5
25 = 5 × 5
35 = 5 × 7
40 = 2 × 2 × 2 × 5
LCM = 1400
Required number = 1400 - 6 = 1394
The the required number is 1394.
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We don’t have your requested question, but here is a suggested video that might help.
the least number such that, when it divided by 15, 25, 35 and 45. it leaves remainder 7, 17, 27 and 37 respectively is