Lithium metal composite oxide, positive electrode active material for lithium secondary battery, positive electrode for lithium secondary battery, and lithium secondary battery

An object of the present invention is to provide a lithium metal composite oxide, when used as a positive electrode active material for a lithium secondary battery, capable of obtaining a lithium secondary battery having a high cycle retention rate, and a positive electrode active material for a lithium secondary battery, a positive electrode for a lithium secondary battery, and a lithium secondary battery in which the lithium metal composite oxide is used. This lithium metal composite oxide is a particulate lithium metal composite oxide, comprising first particles having a particle diameter equal to or less than a 50% cumulative volume particle size Dof the lithium metal composite oxide and second particles having a particle diameter exceeding the D, in which the Dis 2 to 20 μm, an average particle strength Pof the first particles is larger than an average particle strength Pof the second particles, and a standard deviation σof the particle strength of the first particles is larger than a standard deviation σof the particle strength of the second particles.