What is the actual lowest possible positive REAL number
The minimum positive (subnormal) single-precision floating-point value is 2−149 ≈ 1.4 × 10−45. The minimum positive normal value is 2−126 ≈ 1.18 × 10−38 (reference).

DECLARE
    @r1 real = POWER(2e0, -126),
    @r2 real = POWER(2e0, -23)

SELECT
    @r1,
    @r2,
    @r1 * @r2,
    CONVERT(binary(4), @r1 * @r2);


For double-precision, the minimum positive subnormal is:

DECLARE @r1 float = POWER(2e0, -1075);

SELECT @r1, CONVERT(binary(8), @r1);