2,3,4
26,27,28
38,39,40
50,51,52
+12 every time
because they’re all factors of 12 and 12 is the LCM of all 3 numbers.
What if the first is a multiple of 3, the second is a multiple of 4 and the third is a multiple of 5?
3,4,5 LCM=60
63,64,65
123,124,125
183,184,185
243,244,245
What if the first is a multiple of 4, the second is a multiple of 5, and the third is a multiple of 6?
4,5,6 LCM=60
64,65,66
124,125,126
Is there a way to find sets of four consecutive numbers which are multiples of 2, 3, 4 and 5 (in this order)?
2,3,4,5 LCM=60
62,63,64,65
122,123,124,125
182,183,184,185
Or five consecutive numbers which are multiples of 2, 3, 4, 5 and 6 (in this order)?
2,3,4,5,6
62,63,64,65,66
122,123,124,125,126
182,183,184,185,186
Can you use what you have discovered to help you find a few sets of ten consecutive numbers in which:
• the first is a multiple of 1
• the second is a multiple of 2
• the third is a multiple of 3
• the fourth is a multiple of 4
• the fifth is a multiple of 5
• the sixth is a multiple of 6
• the seventh is a multiple of 7
• the eighth is a multiple of 8
• the ninth is a multiple of 9
• the tenth is a multiple of 10?
1,2,3,4,5,6,7,8,9,10 LCM= 2520
2521,2522,2523,2524,2525,2526,2527,2528,2529,2530
5041,5042,5043,5044,5045,5046,5047,5048,5049,5050