Find the greatest number of four digits
which is exactly divisible by 15, 24 and 26
Answers
Answer:
Hey,
The answer is : 9360.
Here is a step - by - step procedure to find the greatest four digit number that is exactly divisible by 15,24,26.
Find the LCM (Least common multiple) of 15, 24, 26. Any number divisible by the LCM of the 15,24,26 will be divisible by each of 15,24,26.
To find LCM, write each number as a product of its prime factors.
15=3∗5 ———————————————15 has one 3 and one 5.
24=2∗2∗2∗3 ———————————24 has three 2’s and one 3.
26=2∗13 ———————————26 has one 2’s and one 13’s.
To get the LCM: Multiply each factor the greatest number of times it occurs in any of the numbers.
LCM =1560
2. To Find the greatest four digit number divisible by 1560:
The greatest four digit number is 9999
9999 when divided by 1560 is 6.40 ( 6.40 is not an integer, thus 9999 is not divisible by 1560. )
The greatest four digit number divided by 1560 would be = 1560∗6=9360
( Note : 6 is the part of the number before the decimal point in 6.04)
3. We can check if 9360 is divisible by each of 15, 24, 36
9360/15=624
9360/24=390
9360/26=360