Chapter 4: Factors and Multiples 55Instead, you’ll want to start by finding the prime factorization of both numbers. Let’s start with
an example with small numbers and then try another with larger numbers.
Suppose you need to find the least common multiple of 12 and 15. Find the prime factorization
of each number.
12 = 2 v 2 v 3
15 = 3 v 5
Identify any common factors. In this example, 12 and 15 both have a factor of 3. Build the LCM
by starting with the common factor or factors, then multiplying by the other factors of 12 and 15
that are not common. 12 and 15 have 3 in common, so that goes into the LCM just once, and then
you collect the other factors of 12, which are 2 v 2, and the other factor of 15, the 5.
LCM = 3 v 2 v 2 v 5
The 3 is the common factor, the two 2s come from the factorization of 12, and the 5 is from the
- Multiply to find that the LCM is 60. 60 is 12 v 5 and 15 v 4, and it’s the smallest multiple 12
and 15 share.
Ready to find the least common multiple of 98 and 168? Start by finding the prime factorization
of each number. You might want to use a factor tree.
98 = 2 v 7 v 7
168 = 2 v 2 v 2 v 3 v 7
The two numbers have a 2 and a 7 in common, so start building the LCM with those.
LCM = 2 v 7 v?
You need another 7 from the 98 and another two 2s and a 3 from the 168.
LCM = 2 v 7 v 7 v 2 v 2 v 3 = 1,176
The multiplication for that one might be challenging, but building lists of multiples up into the
thousands wouldn’t have been an efficient method.
WORLDLY WISDOM
If two numbers are relatively prime, their product will be their LCM.