(1). What is the least LCM of 36 and 27?
9
63
108
972
(2). Write an equivalent expression for 8x + 6 using the distributive property.
2(2x+3)
2(4x+3)
8(x+6)
x(8+6)
An LCM is the least common multiple, so it must be larger than 36 and 27. 63 is obviously not a multiple of 36 and 27. What about 108?
(2)
2(2x+3) = 4X + 6 - No
2(4x+3) = 8X + 6 - Yes -- it's the same as the model
8(x+6) = 8x + 48 - No
x(8+6) = 8x + 6x - No
(1) To find the least common multiple (LCM) of two numbers, you need to factorize the numbers into their prime factors and then select the least power of each prime factor.
For 36, the prime factorization is 2^2 * 3^2.
For 27, the prime factorization is 3^3.
To find the LCM, take the highest power of each prime factor:
- We have 2^2 * 3^3.
So, the LCM of 36 and 27 is 2^2 * 3^3 = 4 * 27 = 108.
Therefore, the correct answer is 108.
(2) The distributive property states that a(b + c) = ab + ac.
Given the expression 8x + 6, we can rewrite it using the distributive property as follows:
8x + 6 = 2 * (4x) + 2 * 3
So, an equivalent expression for 8x + 6 using the distributive property would be 2(4x + 3).
Therefore, the correct answer is 2(4x + 3).