LCM that 8, 10, and 12 is the the smallest number amongst all typical multiples the 8, 10, and 12. The first few multiples the 8, 10, and 12 are (8, 16, 24, 32, 40 . . .), (10, 20, 30, 40, 50 . . .), and also (12, 24, 36, 48, 60 . . .) respectively. There room 3 commonly used techniques to discover LCM of 8, 10, 12 - by listing multiples, by prime factorization, and by division method.

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 1 LCM of 8, 10, and 12 2 List the Methods 3 Solved Examples 4 FAQs

Answer: LCM that 8, 10, and 12 is 120. Explanation:

The LCM of 3 non-zero integers, a(8), b(10), and c(12), is the smallest optimistic integer m(120) the is divisible by a(8), b(10), and c(12) without any remainder.

Let's look at the various methods because that finding the LCM that 8, 10, and 12.

By Listing MultiplesBy division MethodBy prime Factorization Method

### LCM that 8, 10, and 12 by Listing Multiples To calculate the LCM that 8, 10, 12 by listing the end the usual multiples, we have the right to follow the given below steps:

Step 1: list a couple of multiples the 8 (8, 16, 24, 32, 40 . . .), 10 (10, 20, 30, 40, 50 . . .), and also 12 (12, 24, 36, 48, 60 . . .).Step 2: The typical multiples indigenous the multiples that 8, 10, and also 12 room 120, 240, . . .Step 3: The smallest usual multiple of 8, 10, and 12 is 120.

∴ The least typical multiple of 8, 10, and also 12 = 120.

### LCM of 8, 10, and 12 by division Method To calculate the LCM the 8, 10, and also 12 by the division method, we will divide the numbers(8, 10, 12) by your prime factors (preferably common). The product of these divisors gives the LCM that 8, 10, and also 12.

Step 2: If any type of of the provided numbers (8, 10, 12) is a lot of of 2, division it through 2 and write the quotient below it. Carry down any kind of number the is not divisible through the prime number.Step 3: proceed the actions until just 1s space left in the critical row.

The LCM that 8, 10, and 12 is the product of all prime numbers on the left, i.e. LCM(8, 10, 12) by department method = 2 × 2 × 2 × 3 × 5 = 120.

### LCM of 8, 10, and also 12 by element Factorization

Prime administrate of 8, 10, and 12 is (2 × 2 × 2) = 23, (2 × 5) = 21 × 51, and also (2 × 2 × 3) = 22 × 31 respectively. LCM that 8, 10, and 12 deserve to be acquired by multiplying prime components raised to their respective highest possible power, i.e. 23 × 31 × 51 = 120.Hence, the LCM that 8, 10, and 12 by element factorization is 120.

Example 3: Verify the relationship in between the GCD and LCM of 8, 10, and 12.

Solution:

The relation in between GCD and LCM of 8, 10, and also 12 is provided as,LCM(8, 10, 12) = <(8 × 10 × 12) × GCD(8, 10, 12)>/⇒ prime factorization the 8, 10 and also 12:

8 = 2310 = 21 × 5112 = 22 × 31

∴ GCD of (8, 10), (10, 12), (8, 12) and also (8, 10, 12) = 2, 2, 4 and 2 respectively.Now, LHS = LCM(8, 10, 12) = 120.And, RHS = <(8 × 10 × 12) × GCD(8, 10, 12)>/ = <(960) × 2>/<2 × 2 × 4> = 120LHS = RHS = 120.Hence verified. ## FAQs on LCM that 8, 10, and 12

### What is the LCM of 8, 10, and 12?

The LCM that 8, 10, and 12 is 120. To find the least typical multiple of 8, 10, and 12, we require to uncover the multiples the 8, 10, and 12 (multiples the 8 = 8, 16, 24, 32 . . . . 120 . . . . ; multiples of 10 = 10, 20, 30, 40 . . . . 120 . . . . ; multiples the 12 = 12, 24, 36, 48 . . . . 120 . . . . ) and also choose the the smallest multiple the is precisely divisible through 8, 10, and also 12, i.e., 120.

### How to discover the LCM of 8, 10, and 12 by prime Factorization?

To find the LCM of 8, 10, and also 12 utilizing prime factorization, we will uncover the prime factors, (8 = 23), (10 = 21 × 51), and (12 = 22 × 31). LCM that 8, 10, and also 12 is the product of prime factors raised to your respective highest exponent amongst the number 8, 10, and also 12.⇒ LCM the 8, 10, 12 = 23 × 31 × 51 = 120.

### What is the Relation in between GCF and also LCM the 8, 10, 12?

The adhering to equation have the right to be provided to express the relation between GCF and also LCM the 8, 10, 12, i.e. LCM(8, 10, 12) = <(8 × 10 × 12) × GCF(8, 10, 12)>/.

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### Which of the adhering to is the LCM the 8, 10, and also 12? 25, 24, 120, 11

The value of LCM the 8, 10, 12 is the smallest typical multiple the 8, 10, and 12. The number satisfying the given problem is 120.