LCM that 8, 10, and also 12 is the the smallest number among all usual multiples the 8, 10, and 12. The first couple of multiples of 8, 10, and also 12 are (8, 16, 24, 32, 40 . . .), (10, 20, 30, 40, 50 . . .), and also (12, 24, 36, 48, 60 . . .) respectively. There room 3 typically used techniques to uncover LCM the 8, 10, 12 - through listing multiples, by element factorization, and by department method.

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1.LCM the 8, 10, and also 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 at the different methods because that finding the LCM that 8, 10, and also 12.

By Listing MultiplesBy department MethodBy element Factorization Method

LCM the 8, 10, and 12 through Listing Multiples

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To calculate the LCM of 8, 10, 12 by listing the end the typical multiples, we deserve 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 12 (12, 24, 36, 48, 60 . . .).Step 2: The usual multiples native the multiples the 8, 10, and 12 space 120, 240, . . .Step 3: The smallest common multiple of 8, 10, and also 12 is 120.

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

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

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To calculation the LCM the 8, 10, and 12 through the division method, we will certainly divide the numbers(8, 10, 12) by their prime determinants (preferably common). The product of these divisors offers the LCM the 8, 10, and also 12.

Step 2: If any kind of of the given numbers (8, 10, 12) is a lot of of 2, division it by 2 and write the quotient listed below it. Lug down any type of number that is not divisible through the element number.Step 3: continue the measures until just 1s space left in the last row.

The LCM of 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 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 the 8, 10, and also 12 can be acquired by multiply prime determinants raised to your respective highest possible power, i.e. 23 × 31 × 51 = 120.Hence, the LCM the 8, 10, and 12 by element factorization is 120.

☛ additionally Check:


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

Solution:

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

8 = 2310 = 21 × 5112 = 22 × 31

∴ GCD of (8, 10), (10, 12), (8, 12) and (8, 10, 12) = 2, 2, 4 and also 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 on LCM the 8, 10, and also 12

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

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

How to uncover the LCM of 8, 10, and also 12 by element Factorization?

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

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

The complying with equation deserve to be provided to to express the relation between GCF and also LCM of 8, 10, 12, i.e. LCM(8, 10, 12) = <(8 × 10 × 12) × GCF(8, 10, 12)>/.

See more: Which Of The Following Results In A Decrease In The Entropy Of The System?

Which that the complying with is the LCM the 8, 10, and 12? 25, 24, 120, 11

The worth of LCM the 8, 10, 12 is the smallest typical multiple the 8, 10, and 12. The number to solve the given problem is 120.