A natural number when divided by 12,15,18 leave remainder 5,8,11 respectively.Find sum of the digits of least such number?
A)9
B)10
C)11
D)12
Answers
Step-by-step-Explanation:
Given: A natural number when divided by 12,15,18 leave remainder 5,8,11 respectively.
To find: Find sum of the digits of least such number?
A)9
B)10
C)11
D)12
Solution:
Step 1: Find LCM of 12, 15 and 18
Write prime factors of each number
12=2×2×3
15=3×5
18=2×3×3
LCM(12,15,18)= 2²×3²×5
LCM(12,15,18)= 4×9×5
LCM(12,15,18)= 180
Step 2: Find difference of each remainder from respective number
12-5=7
15-8=7
18-11=7
since, difference of each remainder is same.
Step 3: Subtract the difference of remainder from 180.
The natural number is 180-7=173
Step 4: Find sum of digits of 173
1+7+3=11
Option C is correct.
Final answer:
173 when divided by 12,15,18 leave remainder 5,8,11 respectively.
Sum of the digits of least such number is 11.
Option C is correct.
Hope it helps you.
To learn more on brainly:
4. find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.
https://brainly.in/question/5766301
Three friends went to a hotel and had breakfast to their taste, paying Rs.16, Rs.17 and Rs.21 respectively
(i) Find the...
https://brainly.in/question/4835608
Answer:
Step-by-step explanation:
Solution:
Step 1: Find LCM of 12, 15 and 18
Write prime factors of each number
12=2×2×3
15=3×5
18=2×3×3
LCM(12,15,18)= 2²×3²×5
LCM(12,15,18)= 4×9×5
LCM(12,15,18)= 180
Step 2: Find difference of each remainder from respective number
12-5=7
15-8=7
18-11=7
since, difference of each remainder is same.
Step 3: Subtract the difference of remainder from 180.
The natural number is 180-7=173
Step 4: Find sum of digits of 173
1+7+3=11
Option C is correct.
Final answer:
173 when divided by 12,15,18 leave remainder 5,8,11 respectively.
Sum of the digits of least such number is 11.
Correct option is C