15. Which of the following is divisible by all of the integers from 1 to 10 inclusive?
A $23 \times 34$
B $34 \times 45$
C $45 \times 56$
D $56 \times 67$
E $67 \times 78$
15. C Of the options given, $23 \times 34,56 \times 67$ and $67 \times 78$ are all not divisible by 5 , so may be discounted. Also 34 is not divisible by 4 and 45 is odd, so $34 \times 45$ may also be discounted as it is not divisible by 4 . The only other option is $45 \times 56$. As a product of prime factors, $45 \times 56=2^{3} \times 3^{2} \times 5 \times 7$, so it is clear that it is divisible by all of the integers from 1 to 10 inclusive.