



 
Hi Peggy, Let me try a slightly smaller problem.
First I want to write 4, 5 and 6 as a product of primes
I need a way to refer to the number I am looking for, the smallest number divisible by each of 4, 5 and 6, so I am going to call it N. I am going to construct N in terms of its prime factors. Since 4 = 2 × 2 divides N, N must have 2 as a prime factor twice.
5 must also divide N so 5 must be a prime factor of N.
Finally 6 = 2 × 3 must divide N so 2 and 3 are prime factors of N. I already have a 2 in the construction of N so all I need to add is a 3
Seeing N in this form it is easy to see that 4 = 2 × 2, 5 and 6 = 2 × 3 all divide N and leaving any of the 4 primes out of the construction of N will mean that one of 4, 5 or 6 will not divide N. Thus N = 2 × 2 × 5 ×3 = 60 is the smallest number divisible by each of 4, 5 and 6. Now try this procedure with 1, 2, 3, 4, 5, 6, 7, 8 and 9. Penny  


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