Question

Find the smallest number that divides 13 and 8 leaving remainder 1 and 2 respectively. Please solve it. I need Step by Step explanation.

Answer 1

ANSWER:

• The smallest number = - 3

GIVEN:

• A number divides 13 and 8 leaving remainder 1 and 2 respectively.

TO FIND:

• The smallest number.

EXPLANATION:

The remanider when it divides the 13 is 1

The remanider when it divides the 8 is 2

By factorizing 8

8 = 2 × 2 × 2

x - 2 = 1(The remainder when 13 is divided by the number )

x = 3

By factorizing 13

13 = 1 × 13

Take one as it is the smallest number.

x - 1 = 2(The remainder when 8 is divided by the number )

x = 3

Take L.C.M for 3 and 3

L.C.M = 3

If natural numbers are considered 3 is smallest number and when integers are considered - 3 is smallest number.

VERIFICATION:

13 / - 3 = - 4 --> Remainder = 1

8 / - 3 = -2 --> Remainder = 2

HENCE VERIFIED.