What is the LCM of 5 and 15 using prime factorization?

The Least Common Multiple (LCM) of 5 and 15 is 15. Here's how to find it using prime factorization:

Prime factorization involves breaking down each number into its prime factors.

• 5 = 5 (5 is already a prime number)
• 15 = 3 x 5

To find the LCM, we take the highest power of each prime factor that appears in either factorization:

• The prime factors involved are 3 and 5.
• The highest power of 3 is 3¹ (from the factorization of 15).
• The highest power of 5 is 5¹ (appears in both 5 and 15).

Therefore, the LCM is: 3 x 5 = 15.

As the reference points out, multiples of 5 are 5, 10, 15, 20... and multiples of 15 are 15, 30, 45... The smallest multiple that is divisible by both 5 and 15 is 15.