Find the smallest natural number that has a remainder 3 when divided by 5, a remainder 5 when divided by 7, and a remainder 8 when divided by 10.

68

Step-by-step explanation:

"a remainder 3 when divided by 5": The number must be 3 more than a multiple of 5.

"a remainder 5 when divided by 7": The number must be 5 more than a multiple of 7.

"a remainder 8 when divided by 10": The number must be 8 more than a multiple of 10.

List some number that are 8 more than a multiple of 10:

18, 28, 38, 48, 58, 68, 78, 88, 98

List some number that are 5 more than a multiple of 7:

12, 19, 26, 33, 40, 47, 54, 61, 68, 75

We see 68 as a the lowest common multiple.

68/5 = 13 remainder 3

68