Answer:
1. 10218
2. 9720
Step-by-step explanation:
1 ---------------
need to find the least 5 -digit number leaving same remainder when divided by 12, 18, 21, 28
- 12= 2x2x3
- 18=2x3x3
- 21= 3x7
- 28= 2x2x7
- LCM(12,18, 21,28)= 2x2x3x3x7= 262
Least 5-digit number is 10000, when it is divided by 262, we get
10000/262= 38.17
39*262= 10218, this number leaves 0 remainder when divided by all 4 given numbers, any number leaving more remainder will be greater than this
Answer: 10218
2 -----------------
Greatest 4-digit number exactly divisible by 12, 18, 40, 45
- 12=2x2x3
- 18=2x3x3
- 40=2x2x2x5
- 45=3x3x5
- LCM(12,18,40,45)= 2x2x2x3x3x5=360
Greatest 4 digit number is 9999
9999/360= 27.78
360*27= 9720 is the greatest number we are looking for
Answer: 9720
