Question

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.​

Answer 1

Answer:

125

Step-by-step explanation:

Answer 2

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.