The product of two 2-digit numbers is 2160 and their H.C.F. is 12. The numbers are
(36, 60)
Let the two 2-digit numbers be a and b. Their product is 2160, so a x b = 2160. Their H.C.F. is 12. We know that the product of two numbers is equal to the product of their H.C.F. and L.C.M. Therefore, a x b = H.C.F.(a, b) x L.C.M.(a, b). Substituting the given values, we get 2160 = 12 x L.C.M.(a, b). This gives us L.C.M.(a, b) = 180. Now, we look for pairs of 2-digit numbers with an H.C.F. of 12 and an L.C.M. of 180. Checking the options, only 36 and 60 satisfy these conditions: H.C.F.(36, 60) = 12 and L.C.M.(36, 60) = 180. Also, 36 x 60 = 2160.
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