Find the greatest four digit number which exactly divisible by 15 ,24and 36e
Answers
Answer:
Step-by-step explanation:
he answer is : 9720.
9720.
Here is a step - by - step procedure to find the greatest four digit number that is exactly divisible by 15,24,36.
15
,
24
,
36.
Find the LCM (Least common multiple) of 15, 24, 36. Any number divisible by the LCM of the 15,24,36 will be divisible by each of 15,24,36.
15
,
24
,
36.
To find LCM, write each number as a product of its prime factors.
15=3∗5
15
=
3
∗
5
———————————————15 has one 3 and one 5.
24=2∗2∗2∗3
24
=
2
∗
2
∗
2
∗
3
———————————24 has three 2’s and one 3.
36=2∗2∗3∗3
36
=
2
∗
2
∗
3
∗
3
———————————36 has two 2’s and two 3’s.
To get the LCM: Multiply each factor the greatest number of times it occurs in any of the numbers.
There are 3 factors : 2,3,5
2
,
3
,
5
The greatest number of times 2 occurs in the numbers (15, 24, 36) : Three
The greatest number of times 3 occurs in the numbers (15, 24, 36) : Two
The greatest number of times 5 occurs in the numbers (15, 24, 36) : One
LCM =2∗2∗2∗3∗3∗5=360
2
∗
2
∗
2
∗
3
∗
3
∗
5
=
360
2. To Find the greatest four digit number divisible by 360:
The greatest four digit number is 9999
9999
9999 when divided by 360 is 27.75 ( 27.75 is not an integer, thus 9999 is not divisible by 360. )
The greatest four digit number divided by 360 would be = 360∗27=9720
360
∗
27
=
9720
( Note : 27 is the part of the number before the decimal point in 27.75)
3. We can check if 9720 is divisible by each of 15, 24, 36
9720/15=648
9720
/
15
=
648
9720/24=405
9720
/
24
=
405
9720/36=270
9720
/
36
=
270