Question

How to find least common multiples steps

Answer 1

1. State the product of prime factors of each number, not in index form.
2. Write all the prime factors into the Venn diagram for each number.
3. Multiply each prime factor in the Venn diagram to find the LCM.

Answer 2

1. Find the prime factorizations of the numbers.

2. The LCM is the product of common and not common factors with the larger exponent.

Example:

Find the LCD of 108 and 180.

Step 1. First we find the prime factorization of each number.

108 = 2² × 3³

180 = 2² × 3² × 5

Step 2. First, we need common factors with larger exponent.

2² and 2² have the same exponent, 2, so we use 2².

3² and 3² have exponents 2 and 3, so we use the one with the larger exponent 3³.

Now we need the not common factors. 5 is not a common factor since only 180 has it, but you use it too.

The LCD is the product of these factors we just found.

LCD = 2² × 3³ × 5

LCD = 4 × 27 × 5

LCD = 540