Factor each of the denominators into primes. For example, if you are adding or subtracting two fractions, one with a denominator of 30 and the other with a denominator of 45, 30 would be factored into 2 x 3 x 5 and 45 would be factored into 3 x 3 x 5.
Count the number of times each prime is present in each of the factorizations. For example, 30 would have one 2, one 3, and one 5, and 45 would have two 3s and one 5.
Take the greatest number of appearances for each prime number. For example, the most 2s from either denominator is one, so take one 2. The most 3s from either denominator is two, so take two 3s. The most 5s from either denominator is one, so take one 5. List the numbers 2, 3, 3 and 5. Multiply the list together to acquire the lowest common denominator. For example, 2 x 3 x 3 x 5 = 90. The lowest common denominator for 30 and 45 is 90.