The H.C.F. Of two numbers is 12 and their product is 2160. Find their L.C.M​

2 thoughts on “The H.C.F. Of two numbers is 12 and their product is 2160. Find their L.C.M​”

1. Step-by-step explanation:

   Let the numbers be 12x and 12y, where x and y are co-primes.

   Product of the numbers = 144xy

   144xy=6336

   xy=44

   44 can be written as the product of two factors in three ways, i.e., 1×44,2×22,4×11

   As x and y are relatively prime, (x,y) can be (1,44) or (4,11) but not (2,22).

   Hence two possible pairs exist.

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2. [tex] \: \huge\colorbox{pink}{Question}[/tex]

   The H.C.F. Of two numbers is 12 and their product is 2160. Find their L.C.M

   [tex] \: \huge\colorbox{pink}{Recommended Answer}[/tex]

   Product of two numbers = H.C.F × L.C.M

   [tex] \: ⇒ \: \: \: \: \: \: 2160 = 12 \times L.C.M[/tex]

   [tex] \: ⇒ \: \: \: \: \: L.C.M \: = \frac{2160}{12} = 180[/tex]

   Thus, the L.C.M of Two Numbers is 180

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