Leveraging and Energizing America's Apprenticeship Programs Act or the LEAP Act This bill allows employers a business-related tax credit of $1,500 for hiring an apprenticeship employee who has not attained age 25 at the close of the taxable year or $1,000 for hiring an apprenticeship employee who has attained age 25. The credit is available for no more than two taxable years with respect to any apprenticeship employee. An apprenticeship employee is any employee who is employed by an employer in an officially recognized apprenticeable occupation and pursuant to an apprentice agreement registered with the Office of Apprenticeship of the Employment and Training Administration of the Department of Labor or a state apprenticeship agency. As an offset to the cost of this bill, the Office of Management and Budget shall coordinate with federal department heads and independent agencies to impose limits on government printing costs.