Least Common Multiple

How to find the least common multiple of the given numbers and monomials: 2 examples and their solutions.

Example 1

Example

Solution

Finding the least common multiple
is quite similar to
finding the greatest common factor.

Find the prime factorization of 18 and 60.

18 = 2⋅32
60 = 22⋅3⋅5

Write 18 = 2⋅32.
Write 60 = 22⋅3⋅5 in the next line.

Then find the LCM:
the least common multiple.

Compare the same base powers
and write the greater exponent power
in the LCM.

18 has 2.
60 has 22.
So write, the greater exponent power, 22.

18 has 32.
60 has 3.
So write, the greater exponent power, 32.

18 doesn't have 5.
60 has 5.
So write, the greater exponent power, 5.

So the LCM of 18 and 60 is
22⋅32⋅5.

22 = 4
32 = 9

4⋅5 = 20

20⋅9 = 180

So 180 is the least common multiple of 18 and 60.

Example 2

Example

Solution

Write the prime factorizations of the monomials.

Write 6a3c = 2⋅3⋅a3⋅c.
Write 2a2bc2 = 2⋅a2⋅b⋅c2 in the next line.

Compare the same base powers
and write the greater exponent power
in the LCM.

6a3c has 2.
2a2bc2 also has 2.
So write 2.

6a3c has 3.
2a2bc2 doesn't have 3.
So write, the greater exponent power, 3.

6a3c has a3.
2a2bc2 has a2.
So write, the greater exponent power, a3.

6a3c doesn't have b.
2a2bc2 has b.
So write, the greater exponent power, b.

6a3c has c.
2a2bc2 has c2.
So write, the greater exponent power, c2.

So the least common multiple of 6a3c and 2a2bc2 is
2⋅3⋅a3⋅b⋅c2.

2⋅3 = 6

So 2⋅3⋅a3⋅b⋅c2
= 6a3bc2.

So the least common multiple of 6a3c and 2a2bc2 is
6a3bc2.