Find the smallest 4 digit number exactly divisible by 16, 20 and 32.
Answers
Answer:
1120
Step-by-step explanation:
STEP 1 = Find the LCM of 16, 20, and 32 2/ 16 20 32
LCM = 2 x 2 x 2 x 2 x 2 x 5 = 160 2/ 8 10 16
STEP 2 = The largest 4 digit number 2/ 4 5 8
which is a multiple of 160 2/ 2 5 4
Multiples of 160 are: 1 5 2
160 x 1 = 160
160 x 2 = 320
160 x 3 = 480
160 x 5 = 640
160 x 6 = 960
160 x 7 = 1120
The smallest 4 digit number exactly divisible by 16, 20 and 32 is 1120.
Concept used:
- First find the LCM of the given numbers. Then divide the smallest number of 4 digits by the LCM.
- To find the smallest number of four digits which is exactly divisible by the given numbers = smallest four digit number - remainder + LCM
Given:
Number - 16,20 and 32
To find:
The smallest 4 digit number exactly divisible by 16, 20 and 32.
Solution:
Step 1: Find the LCM of 16,20 and 32:
To find the smallest number of 4 digit we have to find the L.C.M of 16, 20 and 32
2 ∣16,20,32
2 ∣8,10,16
2 ∣4,5,8
2 ∣2,5,4
2 |1, 5, 2
5 | 1, 5 , 1
1, 1, 1
L.C.M.of 16, 20,32 = 2 × 2 × 2 × 2 × 2 × 5 = 160
Step 2: Divide the smallest number of 4 digit 1000 by the LCM 160:
We know that the smallest number of four digits = 1000
1000 ÷ 160
1000 = 160 × 6 + 40
Remainder = 40
Step 3: Find the smallest number of four digit which is exactly divisible by 16,20,and 32:
Required number = Smallest four digit number - remainder + LCM
Required number = 1000 - 40 + 160
Required number = 960 + 160
Required number = 1120
Hence, the smallest number of four digits which is divisible by 16,20,and 32 is 1120.
Learn more on Brainly:
What is the greatest 4 digit number which is exactly divisible by 12 18 40 45
https://brainly.in/question/1593980
Find the least number which when divided by 12,16,24 and 36 leaves a remainder 7 in each case.
https://brainly.in/question/520909
#SPJ3
