Find the least common multiple (LCM) of a double-digit and a single digit number. There are two methods you can use to find the LCM. Both methods will work, but you may prefer to use one over the other in certain cases.

*Method 1:*

*Use this method when the two numbers are relatively small (less than 10). *

1. List the multiples of each number.

2. Find the smallest multiple that appears in both lists.

*Method 2:*

*Use this method when the two numbers are large. *

1. Factor each of the numbers into prime numbers.

2. Multiply the prime factors of the two numbers together. *Note: If the two numbers have the same prime factor, only multiply by the maximum number of times that the prime factor appears for the factorization of one number. (See Example 1 below.)

Fill in the answer box with the result.

Find the LCD of 14 and 35.

**Solution:**

*Method 1:*

1. Multiples of **14** are 14, 28, 42, 56, **70**, 84…

Multiples of **35** are 35, **70**, 105, 140…

2. Find the smallest multiple that appears in each list.

*Method 2:*

1. Prime factors of **14** are 7 and 2.

Prime factors of **35** are 7 and 5.

2. Multiply the prime factors of the two numbers together: 2 x 5 x 7

*Note: Since 7 is a prime factor of both 14 and 35, we only multiply by 7 once, which is the maximum number of times that it appears in the factorizations of either 14 or 35.

**Answer** = 70

Find the LCD of 3 and 16.

**Solution:**

*Method 1:*

1. Multiples of **3** are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, **48**…

Multiples of **16** are 16, 32, **48**, 64, 80, 96…

2. Find the smallest multiple that appears in each list.

*Method 2:*

1. Prime factor of **3** is 3.

Prime factors of **16** are 4 and 4.

2. Multiply the prime factors of the two numbers together: 3 x 4 x 4

**Answer** = 48