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The number of lunar craters with a diameter greater than 15 km and an age not exceeding 1.1 billion years was obtained smaller by a factor of several than the number of craters that could have formed over 1.1 billion years if the number of near-Earth objects with a diameter greater than 1 km and their orbital elements during this time were close to their present values. The number of such craters per unit of surface for the region of the Ocean of Storms (Oceanus Procellarum) and the seas on the visible side of the Moon is greater by a factor of several than for the entire surface of the Moon. In our estimates of the number of craters formed as a result of collisions of NEOs with the Moon, we used the values of the characteristic times that elapsed before the collisions of objects colliding with the Moon, and the dependence of the diameters of the craters on the diameters of the impactors that formed these craters. Our estimates do not contradict to the increase in the number of near-Earth objects after possible catastrophic destruction of large asteroids of the main belt, which could have occurred over the past 300 million years.