Question

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

Answer 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.

Answer 2

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

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

$\: ⇒ \: \: \: \: \: \: 2160 = 12 \times L.C.M$

$\: ⇒ \: \: \: \: \: L.C.M \: = \frac{2160}{12} = 180$

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