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In 100 numbers you can select 50 all odd or 50 all even and there will be no consecutive pair. Picking another number must be of the opposite parity and so consecutive with one of your first 50.

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Q: Show that if we select 51 distinct numbers from 1 to 100 at least two are consecutive numbers.?

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The least of the three numbers is 199.

Consecutive numbers can't both be multiples of 7. The LCM of consecutive numbers is their product. 14 and 15 are consecutive numbers whose LCM is a multiple of 7 that is greater than 200.

The LCM of two consecutive numbers is their product. The LCM of two consecutive multiples of 5 is their product divided by 5. Two consecutive numbers cannot be multiples of 5.

No, because every other number in the number line is odd so therefore if you have any number of consecutive numbers you will have at least one odd number (if you're talking about consecutive numbers on a number line).

The least of the three integers is 26.

Yes because at least one of the consecutive numbers will be even, and if you times anything by an even number, the answer will always be even

No. Any three consecutive numbers will have at least one of them which is divisible by 2, which means it cannot be prime. And since 1 is not considered a prime number, it cannot happen.

Zero. Any five consecutive natural numbers will contain at least one multiple of 2 and at least one multiple of 5, meaning that the product will be a multiple of 10.

Every sixth number will be a multiple of 6, so you need at least six consecutive numbers to guarantee that one of them will be divisible by 6.

Least common multiple of two consecutive numbers is always equal to their product. Since 27 & 28 are consecutive numbers, therefore LCM(27, 28) = 27 x 28 = 756.

Select ALL pairs of numbers that have a least common multiple of 30

Consecutive numbers wouldn't both be multiples of 7. If you mean consecutive multiples of 7, the LCM of 210 and 217 is 6510 which is their product divided by 7.

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