Multiple Surprises

Sequences of multiples keep cropping up...
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Multiple Surprises printable worksheet



Here are some challenges involving consecutive numbers and multiples.

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Multiple Surprises
Can you find three consecutive numbers where the first is a multiple of 2, the second is a multiple of 3 and the third is a multiple of 4?

Can you find several examples?

What do you notice?

Can you explain your findings?

What if the first is a multiple of 3, the second is a multiple of 4 and the third is a multiple of 5?

What if the first is a multiple of 4, the second is a multiple of 5, and the third is a multiple of 6?

Is there a way to find sets of four consecutive numbers which are multiples of 2, 3, 4 and 5 (in this order)?

Or five consecutive numbers which are multiples of 2, 3, 4, 5 and 6 (in this order)?



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?



With thanks to Don Steward, whose ideas formed the basis of this problem.