Question

which two consecutiven even numbers have an LCM of 112?​

Answer 1

Answer:

What is the LCM of two consecutive even numbers?

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3 Answers



Amitabha Tripathi

, knows a few computational short-cuts

Answered 4 years ago · Author has 3.6K answers and 6.9M answer views

Note that consecutive even integers 2n2n, 2n+22n+2 have gcd(2n,2n+2)=2gcd(n,n+1)=2gcd(2n,2n+2)=2gcd(n,n+1)=2. Therefore lcm[2n,2n+2]=12(2n)(2n+2)=2n(n+1)lcm[2n,2n+2]=12(2n)(2n+2)=2n(n+1), which is the same as half the product of the integers. ■