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The product of the two numbers is 432, the least common multiple is 144, and the greatest common factor of the two numbers is ()
Formula: product of two numbers = least common multiple multiplied by greatest common factor. Greatest common factor = 3
The product of the greatest common factor and the least common multiple of a number is 144. What is the number
The greatest common factor and the least common multiple of a number are itself, and 144 = 12 × 12
So the number is 12
How to prove that the product of two numbers is equal to the product of the greatest common factor and the least common multiple
Let the greatest common factor of two numbers be X
Then: the two numbers can be expressed as: ax, BX, where a and B are coprime
So: the least common multiple of ax, BX = ABX
And: X * (ABX) = (AX) * (BX)
That is: the product of two numbers is equal to the product of the greatest common factor and the least common multiple
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