The purpose of this study is to learn more about ways to prevent or delay relapse of multiple myeloma (MM). This study will determine the best dosing schedule of LBH589 maintenance therapy as well as the safety (side effects) and tolerability of LBH589 maintenance therapy after autologous hematopoietic cell transplant (HCT).

Inclusion Criteria:

• Adult patients, age ≥ 18 years old
• Ability to provide written informed consent obtained prior to participation in the study and any related procedures being performed
• Histologically confirmed diagnosis of multiple myeloma
• Meeting the Criteria for Symptomatic Multiple Myeloma (CRAB criteria) before the initiation of systemic chemotherapy
• Received high-dose melphalan (≥ 140 mg/m^2) followed by autologous HCT based on the institutional guidelines and within +45 and +180 after autologous HCT at the time of panobinostat maintenance initiation
• Must have achieved at least partial response (PR) prior to autologous HCT and must not have progressive disease (PD) prior to the initiation of maintenance therapy
• Must meet the following laboratory criteria (prior to the initiation of panobinostat maintenance): Absolute neutrophil count (ANC) ≥ 1 x 10^9/L; Hemoglobin ≥ 8 g/dl; Platelets ≥ 50 x 10^9/L (without transfusion support); Creatinine clearance ≥ 40 ml/min or serum creatinine ≤ 2.5 x upper limit of normal (ULN); aspartate aminotransferase (AST) and alanine aminotransferase (ALT) ≤ 2.5 x ULN; Serum bilirubin ≤ 1.5 x ULN; Albumin > 3.0 g/dl; Clinically euthyroid. Note: Participants are permitted to receive thyroid hormone supplements to treat underlying hypothyroidism.
• Baseline (pre-HCT) multigated acquisition (MUGA) or echocardiogram (ECHO) must demonstrate left ventricular ejection fraction (LVEF) ≥ the limit of normal (LLN) of the institutional normal
• Eastern Cooperative Oncology Group (ECOG) Performance Status of ≤ 2 or Karnofsky performance status ≥ 70%
• Prior histone deacetylase (HDAC), deacetylase (DAC), HSP90 inhibitors or valproic acid for the treatment of cancer is allowed

Exclusion Criteria:

• Potential participants who have purely non-secretory multiple myeloma (i.e., the absence of a measurable protein in serum by electrophoresis and immunofixation and the absence of Bence-Jones protein in the urine defined by use of electrophoresis and immunofixation)
• Prior allogeneic HCT
• Prior solid organ transplant requiring immunosuppressive therapy
• Potential participants who will need valproic acid for any medical condition during the study or within 5 days prior to first panobinostat treatment
• Impaired cardiac function or clinically significant cardiac diseases
• Diarrhea > Common Terminology Criteria for Adverse Events (CTCAE) grade 2
• Other concurrent severe and/or uncontrolled medical conditions (e.g., uncontrolled diabetes or active or uncontrolled infection) including abnormal laboratory values, that could cause unacceptable safety risks or compromise compliance with the protocol
• Using medications that have a relative risk of prolonging the QT interval or inducing torsade de pointes if treatment cannot be discontinued or switched to a different medication prior to starting study drug
• Have received targeted agents within 2 weeks or within 5 half-lives of the agent and active metabolites (whichever is longer) and who have not recovered from side effects of those therapies.
• Have received either immunotherapy within < 8 weeks; chemotherapy within < 4 weeks; or radiation therapy to > 30% of marrow-bearing bone within < 2 weeks prior to starting study treatment; or who have not yet recovered from side effects of such therapies
• Have undergone major surgery ≤ 4 weeks prior to starting study drug or have not recovered from side effects of such therapy
• Women who are pregnant or breast feeding or women of childbearing potential (WOCBP) not using an effective method of birth control. WOCBP must have a negative serum pregnancy test within 24 hours of receiving the first dose of study medication.
• Male patients whose sexual partners are WOCBP not using effective birth control
• A prior malignancy with in the last 5 years (except for basal or squamous cell carcinoma, or in situ cancer of the cervix)
• Known positivity for human immunodeficiency virus (HIV) or hepatitis C; baseline testing for HIV and hepatitis C is not required
• Any significant history of non-compliance to medical regimens or unwilling or unable to comply with the instructions given to him/her by the study staff

Adverse events collected from date of consent until off study date, 4 years, 2 months.