LCM of 12 and 15

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LCM is a common multiple, the smallest value between the numbers 12 and 15. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music.

What is the LCM of 12 and 15?

The LCM of 12 and 15 is 60. We can find the LCM using the Listing multiples method, the prime factorization method and the long division method. These are explained below.

LCM of 12 and 15 Using Listing the Multiples

Step1; Write down the multiples of the numbers. Don’t stop too early.

12 = 12,24,48,60 …

15 = 15,60,45,60,75,…

Step 2: Find the smallest number common between the written multiples of 12 and 15

— The smallest common multiple is 60.

Thus, LCM(12,15) = 60

LCM of 12 and 15 Using Prime Factorization

Step 1— factorize the numbers into its prime factors

12 =2×2×3

15 =5×3

Step 2— find the highest powers of the factors of 12 and 15

Step 3— Multiply the highest powers

LCM(12,15) = 60

LCM of 12 and 15 Using Division Method

Write the numbers 12, 15 in a row

Divide them by their common prime factors, if there is one

Carry forward the numbers that are left undivided by the previously chosen factor

Continue dividing until the remainder is ‘1’

Multiply the divisors to find the LCM

LCM(12,15) = 60

Important glossaries on the LCM of 12 and 15

Multiple — product of a number and a natural integer

Prime factor — number one gets after prime factorization any given number

Prime factorization — the process of breaking the number into its prime factors