diff --git a/base/intfuncs.jl b/base/intfuncs.jl
index dc81f2bd3e489..09fb169e08db0 100644
--- a/base/intfuncs.jl
+++ b/base/intfuncs.jl
@@ -96,6 +96,8 @@ end
 
 Least common (positive) multiple (or zero if any argument is zero).
 The arguments may be integer and rational numbers.
+``a`` is a multiple of ``b`` if there exists an integer ``m`` such
+that ``b*m=a``.
 
 ``a`` is a multiple of ``b`` if there exists an integer ``m`` such
 that ``a=mb``.
diff --git a/base/rational.jl b/base/rational.jl
index 69d39770b2095..d9d067b20465d 100644
--- a/base/rational.jl
+++ b/base/rational.jl
@@ -564,8 +564,18 @@ end
 
 float(::Type{Rational{T}}) where {T<:Integer} = float(T)
 
-gcd(x::Rational, y::Rational) = unsafe_rational(gcd(x.num, y.num), lcm(x.den, y.den))
-lcm(x::Rational, y::Rational) = unsafe_rational(lcm(x.num, y.num), gcd(x.den, y.den))
+function gcd(x::Rational, y::Rational)
+    if (isinf(x) && !isinf(y)) || (!isinf(x) && isinf(y))
+        throw(ArgumentError("lcm is not defined"))
+    end
+    return unsafe_rational(gcd(x.num, y.num), lcm(x.den, y.den))
+end
+function lcm(x::Rational, y::Rational)
+    if (isinf(x) && !isinf(y)) || (!isinf(x) && isinf(y))
+        throw(ArgumentError("lcm is not defined"))
+    end
+    return unsafe_rational(lcm(x.num, y.num), gcd(x.den, y.den))
+end
 function gcdx(x::Rational, y::Rational)
     c = gcd(x, y)
     if iszero(c.num)
diff --git a/test/rational.jl b/test/rational.jl
index 90b5414a6fe89..47fac8b4c0e01 100644
--- a/test/rational.jl
+++ b/test/rational.jl
@@ -649,49 +649,24 @@ end
         @test lcm(a, T(0)//T(1)) === T(0)//T(1)
         @test gcdx(a, T(0)//T(1)) === (a, T(1), T(0))
 
-        @test gcdx(T(1)//T(0), T(1)//T(2)) === (T(1)//T(0), T(1), T(0))
-        @test gcdx(T(1)//T(2), T(1)//T(0)) === (T(1)//T(0), T(0), T(1))
-        @test gcdx(T(1)//T(0), T(1)//T(1)) === (T(1)//T(0), T(1), T(0))
-        @test gcdx(T(1)//T(1), T(1)//T(0)) === (T(1)//T(0), T(0), T(1))
         @test gcdx(T(1)//T(0), T(1)//T(0)) === (T(1)//T(0), T(1), T(1))
-        @test gcdx(T(1)//T(0), T(0)//T(1)) === (T(1)//T(0), T(1), T(0))
         @test gcdx(T(0)//T(1), T(0)//T(1)) === (T(0)//T(1), T(0), T(0))
 
         if T <: Signed
-            @test gcdx(T(-1)//T(0), T(1)//T(2)) === (T(1)//T(0), T(1), T(0))
-            @test gcdx(T(1)//T(2), T(-1)//T(0)) === (T(1)//T(0), T(0), T(1))
-            @test gcdx(T(-1)//T(0), T(1)//T(1)) === (T(1)//T(0), T(1), T(0))
-            @test gcdx(T(1)//T(1), T(-1)//T(0)) === (T(1)//T(0), T(0), T(1))
             @test gcdx(T(-1)//T(0), T(1)//T(0)) === (T(1)//T(0), T(1), T(1))
             @test gcdx(T(1)//T(0), T(-1)//T(0)) === (T(1)//T(0), T(1), T(1))
             @test gcdx(T(-1)//T(0), T(-1)//T(0)) === (T(1)//T(0), T(1), T(1))
-            @test gcdx(T(-1)//T(0), T(0)//T(1)) === (T(1)//T(0), T(1), T(0))
-            @test gcdx(T(0)//T(1), T(-1)//T(0)) === (T(1)//T(0), T(0), T(1))
         end
 
         @test gcdx(T(1)//T(3), T(2)) === (T(1)//T(3), T(1), T(0))
         @test lcm(T(1)//T(3), T(1)) === T(1)//T(1)
-        @test lcm(T(3)//T(1), T(1)//T(0)) === T(3)//T(1)
-        @test lcm(T(0)//T(1), T(1)//T(0)) === T(0)//T(1)
-
-        @test lcm(T(1)//T(0), T(1)//T(2)) === T(1)//T(2)
-        @test lcm(T(1)//T(2), T(1)//T(0)) === T(1)//T(2)
-        @test lcm(T(1)//T(0), T(1)//T(1)) === T(1)//T(1)
-        @test lcm(T(1)//T(1), T(1)//T(0)) === T(1)//T(1)
         @test lcm(T(1)//T(0), T(1)//T(0)) === T(1)//T(0)
-        @test lcm(T(1)//T(0), T(0)//T(1)) === T(0)//T(1)
         @test lcm(T(0)//T(1), T(0)//T(1)) === T(0)//T(1)
 
         if T <: Signed
-            @test lcm(T(-1)//T(0), T(1)//T(2)) === T(1)//T(2)
-            @test lcm(T(1)//T(2), T(-1)//T(0)) === T(1)//T(2)
-            @test lcm(T(-1)//T(0), T(1)//T(1)) === T(1)//T(1)
-            @test lcm(T(1)//T(1), T(-1)//T(0)) === T(1)//T(1)
             @test lcm(T(-1)//T(0), T(1)//T(0)) === T(1)//T(0)
             @test lcm(T(1)//T(0), T(-1)//T(0)) === T(1)//T(0)
             @test lcm(T(-1)//T(0), T(-1)//T(0)) === T(1)//T(0)
-            @test lcm(T(-1)//T(0), T(0)//T(1)) === T(0)//T(1)
-            @test lcm(T(0)//T(1), T(-1)//T(0)) === T(0)//T(1)
         end
 
         @test gcd([T(5), T(2), T(1)//T(2)]) === T(1)//T(2)
@@ -699,9 +674,14 @@ end
 
         @test lcm([T(5), T(2), T(1)//T(2)]) === T(10)//T(1)
         @test lcm(T(5), T(2), T(1)//T(2)) === T(10)//T(1)
+
+        @test_throws ArgumentError gcd(T(1)//T(1), T(1)//T(0))
+        @test_throws ArgumentError gcd(T(1)//T(0), T(0)//T(1))
+
+        @test_throws ArgumentError lcm(T(1)//T(1), T(1)//T(0))
+        @test_throws ArgumentError lcm(T(1)//T(0), T(1)//T(1))
     end
 end
-
 @testset "gcdx for 1 and 3+ arguments" begin
     # one-argument
     @test gcdx(7) == (7, 1)