5:What is the smallest of all the natural numbers which leaves a remainder of 7 whenever divided by 11 or 13 or 15 or 17 or 19.
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What is the smallest natural number that, when divided by 20, 42, or 76, leaves a 7-digit leftover in each case
1. Let's say the number is N.
In each scenario, N is divided by 20, 42, or 76, leaving a leftover of 7.
This means that (N-7) is divisible by 20, 42, and 76.
As a result, for the lowest value,
(N−7)=LCM(20,42,76)
=>(N−7)=7980
=>The total number of people is 7987. (Answer)
2. Calculate the LCM of the numbers 20, 42, and 76.
2x2x5 = 20
2x3x7 = 42
2x2x19 = 76
2x2x3x5x7x19 = 7980 is the LCM.
3. The solution is 7987, which is obtained by adding 7 to 7980.
Check for a residue of 7 and a quotient of 7987 divided by 20 = 399. Correct.
The quotient of 7987 divided by 42 is 190, with a remainder of 7. Correct.
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