As there are two consecutive integers then one must be an even number and the other an odd number. If the numbers are y and y + 1 then if y is even, y + 1 is odd and if y is odd then y + 1 is even.
The product of an even integer and an odd integer is always even.
The question therefore has no answer.
121 = 112 but this is not what the question has asked.
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You need at least two numbers to find an LCM. If that's 12 and 11, the LCM of consecutive integers is their product.
They are are 7 and 8.
13 & 15
44 & 45
27 and 28