# How do you find the Least common multiple of #30ab^3, 20ab^3#?

##### 2 Answers

The LCM is

#### Explanation:

The **least common multiple** (or LCM) of two numbers is the product of *the largest amounts of each (prime) factor* that appear in either number. In other words, it is the smallest value that we can guarantee will have both numbers as factors.

**Step 1:** Factor both numbers.

#30ab^3# has the factors#[(2,3,5,a,b^3)]# .

#20ab^3# has the factors#[(2^2, , 5, a, b^3)]# .

**Step 2:** Compare the powers of each factor that appear in both numbers, and circle the one that's bigger.

The factor

#2# appears once in#30ab^3# , and it appears twice in#20ab^3# . Circle the#2^2# .

#[(2,3,5,a,b^3),( (2^2), , 5, a, b^3)]# The factor

#3# appears once in#30ab^3# , and not at all in#20ab^3# . Circle the#3# .

#[(2,(3),5,a,b^3),( (2^2), , 5, a, b^3)]# The remaining three factors

#(5, a, b^3)# appear the same number of times in both numbers. Circle either appearance of these factors.

#[(2,(3),5,a,b^3),( (2^2), , (5), (a), (b^3))]#

**Step 3:** Multiply these circled values together.

The circled values are

#(2^2)(3)(5)(a)(b^3)# . The product of these values is

#60ab^3# This is our least common multiple.

The LCM is

#### Explanation:

The last digit in both 30 and 20 is 0. So the multiple must also end in 0.

The first digits are 3 and 2. The 2 means that they both have to be factors of an even number. The closest even number they both divide exactly into is 6.

6 put with 0 gives 60

Thus the LCM is