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# If the LCM of two numbers is equal to the product of the two numbers, what must be true about their common factor?

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### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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Since LCM(A,B) = (A*B)/(GCF(A,B)), then GCF(A,B) = (A*B)/LCM(A,B).

If the LCM(A,B) = A*B, then GCF(A,B) = (A*B)/LCM(A,B) = (A*B)/(A*B) = 1.
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
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2 numbers don't have any common factors.

LCM (A, B)  = AB/ Gcf

Example :  A = 24 = 23 * 3
B= 36 =  22 * 32

GCF = 22 * 3 = 12  / product of common factors with lowest exponent.

LCM = 23 * 32 = 8(9) = 72  / Equals product of common factors with highest exponent .

LCM = (36) (24)  = 72
12
This means that to find the lowest number which 2 numbers can be divided into that, the greatest
common factor is multiplied only once
Like the above example:

24 = 23 * 3
36 = 22 * 32

between 8 and 4 , 8 =2is divisible both to 8 and 4
Between 3 and 9,  9 = 32 is divisible to both 9 and 3

Their product  8 * 9 = 72 is divisible to both 24, 36.
Which is
(24) (36) = 72
12 (GCF)

If 2 numbers like 22, 45

22 = 2 *11
45 = 32 * 5

Don't have any common factor, therefore , LCM = 22* 45 = 990