Multiple Surprises

Multiple Surprises printable worksheet

Here are some challenges involving consecutive numbers and multiples.

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.