find the least number which when divided by 16,18,20 and,25 leaves 4 remainder in each case but when divided by 7 remain no remainder.
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LCM of 16, 18, 20, 25 = lcm of 2^4 , 2 * 3^2, 2^2 * 5, 5 * 5
= 2^4 * 3^2 * 5 * 5 = 3, 600
so the number N = 3, 600 * x + 4,
3, 600 * x + 4 = 7 * y , x and y are positive integers
y = 514 x + 2x/7 + 4/7
as y is an integer, 2x+4 = multiple of 7.
smallest such number is x = 5
Hence the number N = 3, 600 * 5 + 4 = 18, 004
= 2^4 * 3^2 * 5 * 5 = 3, 600
so the number N = 3, 600 * x + 4,
3, 600 * x + 4 = 7 * y , x and y are positive integers
y = 514 x + 2x/7 + 4/7
as y is an integer, 2x+4 = multiple of 7.
smallest such number is x = 5
Hence the number N = 3, 600 * 5 + 4 = 18, 004
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