Answer:
To find the smallest five-digit number that leaves a remainder of 7 when divided by 32, 18, and 20, we can use the Chinese Remainder Theorem (CRT).
The first step is to find the least common multiple (LCM) of the divisors 32, 18, and 20, which is 2880.
Next, we need to find a number that is congruent to 7 modulo 32, 18, and 20, respectively. We can find these numbers by subtracting 7 from the LCM:
LCM - 7 = 2880 - 7 = 2873.
Thus, the smallest five-digit number that satisfies the given conditions is 2873.
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Answer:
To find the smallest five-digit number that leaves a remainder of 7 when divided by 32, 18, and 20, we can use the Chinese Remainder Theorem (CRT).
The first step is to find the least common multiple (LCM) of the divisors 32, 18, and 20, which is 2880.
Next, we need to find a number that is congruent to 7 modulo 32, 18, and 20, respectively. We can find these numbers by subtracting 7 from the LCM:
LCM - 7 = 2880 - 7 = 2873.
Thus, the smallest five-digit number that satisfies the given conditions is 2873.