LCM that 12 and also 16 is the the smallest number amongst all typical multiples the 12 and also 16. The first few multiples of 12 and also 16 are (12, 24, 36, 48, 60, 72, . . . ) and (16, 32, 48, 64, 80, 96, 112, . . . ) respectively. There room 3 generally used methods to uncover LCM the 12 and also 16 - by element factorization, by listing multiples, and by department method.

You are watching: Least common multiple of 12 and 16

 1 LCM of 12 and 16 2 List the Methods 3 Solved Examples 4 FAQs

Answer: LCM of 12 and 16 is 48.

Explanation:

The LCM of two non-zero integers, x(12) and also y(16), is the smallest confident integer m(48) that is divisible by both x(12) and also y(16) without any type of remainder.

Let's look at the different methods because that finding the LCM the 12 and 16.

By Listing MultiplesBy division MethodBy element Factorization Method

### LCM of 12 and also 16 by Listing Multiples

To calculate the LCM of 12 and 16 by listing out the common multiples, we have the right to follow the given below steps:

Step 1: perform a couple of multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and also 16 (16, 32, 48, 64, 80, 96, 112, . . . . )Step 2: The common multiples from the multiples the 12 and 16 room 48, 96, . . .Step 3: The smallest typical multiple that 12 and also 16 is 48.

∴ The least common multiple the 12 and 16 = 48.

### LCM that 12 and 16 by department Method

To calculate the LCM of 12 and 16 through the department method, we will divide the numbers(12, 16) by your prime components (preferably common). The product of this divisors gives the LCM the 12 and 16.

Step 3: continue the steps until just 1s room left in the last row.

The LCM that 12 and also 16 is the product of all prime numbers on the left, i.e. LCM(12, 16) by division method = 2 × 2 × 2 × 2 × 3 = 48.

See more: What Does It Mean When You Dream Rain Dream Meaning And Interpretations

### LCM the 12 and 16 by prime Factorization

Prime administer of 12 and 16 is (2 × 2 × 3) = 22 × 31 and also (2 × 2 × 2 × 2) = 24 respectively. LCM of 12 and 16 can be derived by multiply prime components raised to their respective highest possible power, i.e. 24 × 31 = 48.Hence, the LCM that 12 and 16 by element factorization is 48.