The purpose of this study is to investigate the safety of a single dose of Lu AF87908, how well it is tolerated and what the body does to the drug in healthy participants and participants with Alzheimer's disease.

The study will be divided into three parts: Part A, Part B and Part C.

Part A consists of up to 6 sequential cohorts (Cohorts A1 to A6):

-Cohorts A1 to A6: 8 healthy participants per cohort (aiming for an equal number of men and women): 6 randomized to Lu AF87908 and 2 randomized to placebo.

Part B consists of up to 3 sequential cohorts (Cohorts B1 to B3):

-Cohorts B1 to B3: 4 Japanese and 4 Chinese healthy participants per cohort: 6 participants randomized to Lu AF87908 and 2 participants randomized to placebo.

Part C consists of 2 sequential cohorts (Cohorts C1 and C4):

-Cohort C1 will consist of 6 participants with Alzheimer's disease with 3:1 randomization scheme for active: placebo. Cohort C4 will consist of up to 8 participants. Cohort C4 participants will be randomized based on the randomization scheme from Cohort C1.

Inclusion criteria

Healthy Participants:

-Men and women ≥18 and ≤65 years of age with a body mass index (BMI) ≥18 and ≤32 kilograms (kg)/square meter (m^2) and a minimum weight of 50 kg.

Participants with Alzheimer's disease:

• Men and women with a clinical diagnosis of Alzheimer's disease, Stages 3-4 according to the FDA guidelines.

• Mini-Mental State Examination (MMSE) of 15-30.

• Clinical Dementia Scale (CDR) global score up to and including 2.0.

• Confirmed or determined (via amyloid positron emission tomography [PET] scan) to be amyloid positive.

• If on FDA approved Alzheimer's disease medication, the treatment has been stable for 4 months prior to Day 1.

  -≥50 years of age.

• BMI ≥18 and ≤40 kg/m^2 and a minimum weight of 50 kg.

Exclusion criteria:

• Clinically relevant structural brain abnormality as assessed using magnetic resonance imaging (MRI).
• Any past or current treatment with an anti-Abeta or anti-tau active vaccine.
• Any past or current treatment with a monoclonal anti-tau antibody or a tau anti-sense oligomer within the last 6 months.
• Treatment with covid-19, influenza or pneumonia vaccine within the last 30 days prior to dosing of investigational medicinal product (IMP).

Other eligibility criteria may apply.