Find the least number which when divided by 6, 15 and 18, leave remainder 5 in each case.


Question: Find the least number which when divided by 6, 15 and 18, leave remainder 5 in each case.

LCM is the smallest positive number that is a multiple of two or more numbers.

Answer: 95 is the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case.

To find the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case we have to do the following steps:

  • Find the LCM of 6, 15 and 18
  • Add 5 in to the LCM 

Explanation:

Below is the LCM shown for 6,15 and 18 using Prime Factorization

6 = 2 × 3

15 = 3 × 5

18 = 2 × 3 × 3

Thus, the LCM of 6,15 and 18 = 2 × 3 × 3 × 5 = 90

Now, adding 5 to 90, we get 90 + 5 = 95

Verification:

1) 95/6
Quotient = 15
Remainder = 5

2) 95/15
Quotient = 6
Remainder = 5

3) 95/18
Quotient = 5
Remainder = 5

Hence, 95 is the least number which when divided by 6, 15 and 18 leaves a remainder 5 in each case.