What Is the Difference Between LCD and LCM?

By Staff WriterLast Updated Apr 17, 2020 10:35:45 AM ET

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.

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.