LCM that 8, 10, and also 12 is the smallest number among all typical multiples of 8, 10, and also 12. The first few multiples the 8, 10, and also 12 room (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 find LCM that 8, 10, 12 - by listing multiples, by element factorization, and by department method.

You are watching: What is the least common multiple of 8 10 and 12

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

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

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Explanation:

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


Let's look in ~ the various methods for finding the LCM that 8, 10, and 12.

By Listing MultiplesBy department MethodBy element Factorization Method

LCM that 8, 10, and also 12 through Listing Multiples

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To calculate the LCM the 8, 10, 12 by listing out the common multiples, we deserve to follow the given below steps:

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

∴ The least common multiple that 8, 10, and 12 = 120.

LCM the 8, 10, and also 12 by division Method

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To calculate the LCM of 8, 10, and 12 through the division method, we will divide the numbers(8, 10, 12) by their prime components (preferably common). The product of this divisors provides the LCM the 8, 10, and also 12.

Step 2: If any type of of the given numbers (8, 10, 12) is a many of 2, divide it by 2 and write the quotient listed below it. Carry down any kind of number the is not divisible through the prime number.Step 3: continue the measures until only 1s room left in the critical row.

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

LCM the 8, 10, and 12 by element Factorization

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

☛ additionally Check:


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

Solution:

The relation between GCD and also LCM of 8, 10, and also 12 is given as,LCM(8, 10, 12) = <(8 × 10 × 12) × GCD(8, 10, 12)>/⇒ element factorization that 8, 10 and 12:

8 = 2310 = 21 × 5112 = 22 × 31

∴ GCD the (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.


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FAQs top top LCM of 8, 10, and 12

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

The LCM that 8, 10, and 12 is 120. To find the least common multiple of 8, 10, and also 12, we require to find the multiples of 8, 10, and also 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 choose the smallest multiple the is precisely divisible by 8, 10, and also 12, i.e., 120.

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

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

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

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

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Which of the following is the LCM of 8, 10, and 12? 25, 24, 120, 11

The value of LCM that 8, 10, 12 is the smallest common multiple of 8, 10, and 12. The number to solve the given problem is 120.