1. N is the least number such that when divided by 180 or 144 the remainder is 7 but when dis
by 7 the remainder is 1. Then which of these is true:
110ZN 1000
Answers
Given : N is the least number such that when divided by 180 or 144 the remainder is 7 but when divided by 7 the remainder is 1
To Find : which of these is true:
1] 0 <N< 1000
2) 1000<N< 2000
3] 2000<N< 4000
4) N> 4000
Solution:
N = 180A + 7
N = 144B + 7
=> N - 7 = 180A = 144B
Hence LCM of 180 & 144
180 = 36 * 5
144 = 36 * 4
=> LCM = 720
=> N = 720C + 7
when divided by 7 the remainder is 1
=> N = 7D + 1
720C + 7 = 7D + 1
=> 7(D - 1) = 720C - 1
=> 7(D - 1) = 7(103)C - C - 1
=> 7(D - 1) = 7(103)C - (C + 1)
=> C + 1 = 7k
k = 1
=> C = 6
N = 720C + 7
= 720 * 6 + 7
= 4327
N> 4000
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Answer:
Step-by-step explanation: