A2 8.2 LCM to LCD

Front

What is the least common multiple (LCM)?

Back

The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the integers.

Front

How do you find the LCM of two monomials, such as 4xy^2 and 10x^3y?

Back

To find the LCM of two monomials, take the highest power of each variable and the LCM of the coefficients. For 4xy^2 and 10x^3y, LCM = 20x^3y^2.

Front

What is the LCM of x² - 3x + 2 and x² - 2x + 1?

Back

The LCM is (x-1)²(x-2).

Front

What is the LCM of x² + x - 12 and x² - 9?

Back

The LCM is (x - 3)(x + 3)(x + 4).

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest common multiple of the denominators of two or more fractions.

Front

How do you find the LCD of fractions like 5/(x+8) and 2x/(x+3)?

Back

To find the LCD, identify the unique factors in the denominators and multiply them. For 5/(x+8) and 2x/(x+3), LCD = (x+8)(x+3).

Front

What is the LCM of 10y² and 15y²?

Back

The LCM is 30y².

Front

What is the relationship between LCM and GCD (Greatest Common Divisor)?

Back

The relationship is given by the formula: LCM(a, b) * GCD(a, b) = a * b.

Front

How can you find the LCM of three numbers, for example, 4, 6, and 8?

Back

Find the LCM of two numbers first, then use that result to find the LCM with the third number. LCM(4, 6) = 12, then LCM(12, 8) = 24.

Front

What is the prime factorization method for finding LCM?

Back

List the prime factors of each number, take the highest power of each prime factor, and multiply them together.