Question

Find the smallest number which when divided by 6,8,12 leaves the same remainder 2 in each case

Answer 1

6. =2*3

8. =2power3

12. =2²*3

LCM=2power3*3

=24

The smallest number is

24+2=26

Answer 2

The smallest number which when divided by 6,8,12 leaves a remainder of 2 in each case is 26.

Concept used:

• To find the least number which when divided by 6,8,12 leaves the remainder 2 in each case, First, we have to find the L.C.M. of 6,8,12 and then add 2 in the L.C.M. of these 3 numbers.
• LCM of two or more numbers = Product of the greatest power of each prime factor involved in the numbers, with the highest power.

Given:

Number that when divided by 6,8,12 leaves a remainder of 2 in each case​.

To find :

The least number

Solution:

Step 1: Find the L.C.M of 6,8,12 by prime factorization method:

6 = 2 × 3  = 2¹ × 3¹

8 = 2 × 2 × 2  = 2³

12 = 2 × 2 × 3 = 2² × 3¹

L.C.M (6,8,12) = 2³ × 3¹

LCM (6,8,12) = 2 × 2 × 2 × 3  = 24

L.C.M of 6 ,8 and 12 = 24

Step 2: Add the remainder to the LCM:

Add remainder 2 to the L.C.M of 6 ,12 and 24 = 24 + 2 = 26

Hence, the least number which when divided by 6,12, and 24 leaves a remainder of 2 in each case is 26.

Learn more on Brainly:

Find the least number which when divided by 12,16,24 and 36 leaves a remainder 7 in each case.

brainly.in/question/520909

Find the smallest number when divided by 161 207 and 184 leaves the remainder 21 in each case

brainly.in/question/3384838

#SPJ3