LCM that 16, 24, and 40 is the the smallest number amongst all usual multiples the 16, 24, and 40. The first few multiples the 16, 24, and also 40 are (16, 32, 48, 64, 80 . . .), (24, 48, 72, 96, 120 . . .), and also (40, 80, 120, 160, 200 . . .) respectively. There are 3 generally used approaches to uncover LCM of 16, 24, 40 - by listing multiples, by department method, and by prime factorization.

You are watching: Lcm of 16 24 and 40

 1 LCM of 16, 24, and 40 2 List the Methods 3 Solved Examples 4 FAQs

Answer: LCM of 16, 24, and 40 is 240. Explanation:

The LCM of three non-zero integers, a(16), b(24), and also c(40), is the smallest confident integer m(240) that is divisible through a(16), b(24), and c(40) without any remainder.

The methods to find the LCM the 16, 24, and also 40 are described below.

By division MethodBy prime Factorization MethodBy Listing Multiples

### LCM that 16, 24, and 40 by department Method To calculate the LCM of 16, 24, and also 40 by the division method, we will divide the numbers(16, 24, 40) by their prime components (preferably common). The product of these divisors provides the LCM the 16, 24, and 40.

Step 2: If any kind of of the given numbers (16, 24, 40) is a multiple of 2, divide it by 2 and also write the quotient below it. Lug down any kind of number the is not divisible by the element number.Step 3: continue the actions until only 1s space left in the last row.

The LCM of 16, 24, and also 40 is the product of every prime number on the left, i.e. LCM(16, 24, 40) by department method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

### LCM the 16, 24, and also 40 by prime Factorization

Prime administer of 16, 24, and also 40 is (2 × 2 × 2 × 2) = 24, (2 × 2 × 2 × 3) = 23 × 31, and also (2 × 2 × 2 × 5) = 23 × 51 respectively. LCM that 16, 24, and 40 can be acquired by multiplying prime determinants raised to their respective highest possible power, i.e. 24 × 31 × 51 = 240.Hence, the LCM the 16, 24, and 40 by prime factorization is 240.

### LCM of 16, 24, and 40 through Listing Multiples

To calculate the LCM the 16, 24, 40 through listing out the typical multiples, we have the right to follow the given below steps:

Step 1: perform a few multiples the 16 (16, 32, 48, 64, 80 . . .), 24 (24, 48, 72, 96, 120 . . .), and 40 (40, 80, 120, 160, 200 . . .).Step 2: The usual multiples native the multiples the 16, 24, and also 40 room 240, 480, . . .Step 3: The smallest usual multiple of 16, 24, and also 40 is 240.

∴ The least typical multiple the 16, 24, and 40 = 240.

☛ likewise Check:

Example 3: Verify the relationship between the GCD and also LCM that 16, 24, and also 40.

Solution:

The relation between GCD and also LCM of 16, 24, and also 40 is offered as,LCM(16, 24, 40) = <(16 × 24 × 40) × GCD(16, 24, 40)>/⇒ prime factorization that 16, 24 and also 40:

16 = 2424 = 23 × 3140 = 23 × 51

∴ GCD that (16, 24), (24, 40), (16, 40) and (16, 24, 40) = 8, 8, 8 and also 8 respectively.Now, LHS = LCM(16, 24, 40) = 240.And, RHS = <(16 × 24 × 40) × GCD(16, 24, 40)>/ = <(15360) × 8>/<8 × 8 × 8> = 240LHS = RHS = 240.Hence verified. ## FAQs on LCM of 16, 24, and also 40

### What is the LCM the 16, 24, and also 40?

The LCM the 16, 24, and 40 is 240. To find the least common multiple (LCM) of 16, 24, and also 40, we need to uncover the multiples the 16, 24, and 40 (multiples of 16 = 16, 32, 48, 64 . . . . 240 . . . . ; multiples of 24 = 24, 48, 72, 96 . . . . 240 . . . . ; multiples that 40 = 40, 80, 120, 160, 240 . . . .) and also choose the the smallest multiple the is exactly divisible through 16, 24, and also 40, i.e., 240.

### What are the approaches to find LCM of 16, 24, 40?

The typically used approaches to discover the LCM of 16, 24, 40 are: