At first we tried to find several examples, starting with the smallest multiples we could find;
x= multiple of 2
y= multiple of 3
z=multiple of 4
n x. y. z.
0. 2. 3. 4
1. 14. 15. 16
2. 26. 27. 28
3. 38. 39. 40
4. 50. 51. 52
5. 62. 63. 64
6. 74. 75. 76
7. 86. 87. 88
8. 98. 99. 100
We recognised that there was a pattern.
-The 10's units go up by one, the single units go up by 2.
-12 is added to each multiple every time. 12 is the lowest common multiple of 2,3 and 4.
We the found that there was a formula for each multiple;
x= 12n+2
y= 12n+3
z= 12n+4
We then developed our formulas to prove that they were the multiples of 2/3/4;
2(6n+1)
3(4n+1)
4(3n+1)
After this we moved on to the next part of the problem, we tried out the multiples of 3,4 and 5.
n. x. y. z
0. 3. 4. 5
1. 63. 64. 65
2. 123. 124. 125
3. 183. 184. 185
4. 243. 244. 245
5. 303. 304. 305
6. 363. 364. 365
7. 423. 424. 425
8. 483. 484. 485
9. 543. 544. 545
We worked out that the multiples gained 60 each time, therefore;
x= 60n+3
y= 60n+4
z= 60n+5
60 is the lowest common multiple of 3,4 and5
to prove this is correct we calculated that;
3(20+1)
4(15+1)
5(12+1)
We are developing our answers to find the four consecutive numbers. We can use the multiples from 3,4 amd5, then add a number either side of it.