The prime factorizations of the denominators of and are given: 10r2 = 2 (5) (r) (r) 4r = 2 (2) (r) What is the LCD of the expressions? 4r2 10r2 20r2 40r2

The LCD of two terms is obtained by multiplying the commonly occurring factors and the non-common factors together. An important thing which must be noted is that the common factor is used only once. For example, in case of 10 and 6. Factors of 10 are 2 and 5, Factors of 6 are 2 and 3. 2 is a common factor and occurs in both terms. While finding the LCD of these 2, 2 will be multiplied just once with the non-common terms. Similar will be the case with given terms.

Common factors of the given terms are 2 and r

Non-common factors of the given terms are 5, r and 2

The LCD of the given two terms will be = 2r * 10r = 20r²

20r² is the smallest number which is divisible by both the given terms.

So, option C gives the correct answer.