Q:

# What is the difference between LCD and LCM?

A:

The lowest common denominator, or LCD, denotes the smallest number divisible by the denominators of every fraction in a set, whereas a least common multiple, or LCM, is the smallest multiple that two numbers have in common as products. Finding the LCD and LCM requires knowing prime factors of a number.

## Keep Learning

For instance, the LCM of 28 and 42 is 84. To find this, both products are broken down into prime factors. The factors for 28 are 2^2 and seven. Denoting 2^2 means two is used twice, so two times two is four, and then four times seven is 28. For 42, the prime factors are two, three and seven. To find the least common multiple, the highest power of each numeral is multiplied together, which is 2^2 times three times seven, or 84.

For the LCD, consider the fractions 7/42 and 5/28. Both 42 and 28 must be broken into their prime factors. Forty-two is two times three times seven. Twenty-eight is 2^2 times seven. Each is factored into two, three and seven. To determine the LCD of 42 and 28, each factor is raised by the highest exponent and multiplied, so that means two is squared. The LCD is 2^2 times three times seven, or 84. The fractions are then converted to 14/84 and 15/84, because 42 times two is 84 and 28 times three is also 84.

Sources:

## Related Questions

• A: To find the least common multiple of two numbers, factor the two numbers, noting the frequency of the prime factors, and then multiply the most repeated fa... Full Answer >
Filed Under:
• A: A fraction is converted to a percentage by first expressing the fraction with a denominator of 100, then writing the numerator with a percent sign behind i... Full Answer >
Filed Under:
• A: Find the common denominator of a set of fractions by identifying the denominators of the fractions, creating a list of the multiples of those denominators,... Full Answer >
Filed Under:
• A: To add fractions, ensure the bottom numbers (denominators) are the same, add the top numbers (numerators), keep the denominator, and simplify the fraction ... Full Answer >
Filed Under:
PEOPLE SEARCH FOR