S000069099 [Member] Expense Example - WESTERN ASSET SMASh SERIES CORE COMPLETION FUND - SMASh SERIES CORE COMPLETION FUND	Feb. 28, 2026 USD ($)
Prospectus [Line Items]
Expense Example, with Redemption, 1 Year	$ 0
Expense Example, with Redemption, 3 Years	37
Expense Example, with Redemption, 5 Years	78
Expense Example, with Redemption, 10 Years	$ 199

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form N-1A
-Section 3
-Subsection instruction
-Paragraph 4

Name:	oef_ExpenseExampleYear01
Namespace Prefix:	oef_
Data Type:	dtr-types:nonNegativeMonetaryItemType
Balance Type:	na
Period Type:	duration

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form N-1A
-Section 3
-Subsection instruction
-Paragraph 4

Name:	oef_ExpenseExampleYear03
Namespace Prefix:	oef_
Data Type:	dtr-types:nonNegativeMonetaryItemType
Balance Type:	na
Period Type:	duration

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form N-1A
-Section 3
-Subsection instruction
-Paragraph 4

Name:	oef_ExpenseExampleYear05
Namespace Prefix:	oef_
Data Type:	dtr-types:nonNegativeMonetaryItemType
Balance Type:	na
Period Type:	duration

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form N-1A
-Section 3
-Subsection instruction
-Paragraph 4

Name:	oef_ExpenseExampleYear10
Namespace Prefix:	oef_
Data Type:	dtr-types:nonNegativeMonetaryItemType
Balance Type:	na
Period Type:	duration

Reference 1: http://www.xbrl.org/2003/role/presentationRef
-Publisher SEC
-Name Form N-1A
-Section 1
-Subsection a

Name:	dei_LegalEntityAxis=lmpinst_S000069099Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Name:	oef_ClassAxis=lmpinst_C000220869Member
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: