LCM of 8, 9, and 10 is the smallest number among all common multiples that 8, 9, and also 10. The first few multiples of 8, 9, and 10 are (8, 16, 24, 32, 40 . . .), (9, 18, 27, 36, 45 . . .), and also (10, 20, 30, 40, 50 . . .) respectively. There space 3 generally used methods to uncover LCM that 8, 9, 10 - by department method, by listing multiples, and by element factorization.

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1.LCM of 8, 9, and 10
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 8, 9, and also 10 is 360.

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Explanation:

The LCM of three non-zero integers, a(8), b(9), and also c(10), is the smallest confident integer m(360) the is divisible through a(8), b(9), and also c(10) without any kind of remainder.


Let's look in ~ the different methods because that finding the LCM of 8, 9, and 10.

By Listing MultiplesBy element Factorization MethodBy division Method

LCM of 8, 9, and 10 through Listing Multiples

To calculation the LCM the 8, 9, 10 by listing the end the typical multiples, we can follow the given listed below steps:

Step 1: list a couple of multiples that 8 (8, 16, 24, 32, 40 . . .), 9 (9, 18, 27, 36, 45 . . .), and 10 (10, 20, 30, 40, 50 . . .).Step 2: The typical multiples from the multiples that 8, 9, and 10 are 360, 720, . . .Step 3: The smallest typical multiple the 8, 9, and also 10 is 360.

∴ The least typical multiple of 8, 9, and also 10 = 360.

LCM the 8, 9, and 10 by prime Factorization

Prime administrate of 8, 9, and also 10 is (2 × 2 × 2) = 23, (3 × 3) = 32, and (2 × 5) = 21 × 51 respectively. LCM that 8, 9, and 10 can be derived by multiplying prime determinants raised to their respective greatest power, i.e. 23 × 32 × 51 = 360.Hence, the LCM the 8, 9, and 10 by prime factorization is 360.

LCM of 8, 9, and also 10 by division Method

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To calculation the LCM the 8, 9, and 10 by the department method, we will divide the numbers(8, 9, 10) by their prime factors (preferably common). The product of these divisors provides the LCM that 8, 9, and also 10.

Step 2: If any of the offered numbers (8, 9, 10) is a many of 2, divide it by 2 and write the quotient listed below it. Lug down any number the is no divisible through the prime number.Step 3: proceed the steps until only 1s space left in the critical row.

The LCM the 8, 9, and also 10 is the product of all prime numbers on the left, i.e. LCM(8, 9, 10) by department method = 2 × 2 × 2 × 3 × 3 × 5 = 360.

☛ likewise Check:


Example 2: find the the smallest number that is divisible through 8, 9, 10 exactly.

Solution:

The value of LCM(8, 9, 10) will be the the smallest number the is precisely divisible through 8, 9, and also 10.⇒ Multiples that 8, 9, and also 10:

Multiples that 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, . . . ., 328, 336, 344, 352, 360, . . . .Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 324, 333, 342, 351, 360, . . . .Multiples that 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 320, 330, 340, 350, 360, . . . .

Therefore, the LCM that 8, 9, and also 10 is 360.


Example 3: Verify the relationship between the GCD and LCM of 8, 9, and 10.

Solution:

The relation in between GCD and also LCM of 8, 9, and 10 is given as,LCM(8, 9, 10) = <(8 × 9 × 10) × GCD(8, 9, 10)>/⇒ element factorization that 8, 9 and 10:

8 = 239 = 3210 = 21 × 51

∴ GCD that (8, 9), (9, 10), (8, 10) and also (8, 9, 10) = 1, 1, 2 and 1 respectively.Now, LHS = LCM(8, 9, 10) = 360.And, RHS = <(8 × 9 × 10) × GCD(8, 9, 10)>/ = <(720) × 1>/<1 × 1 × 2> = 360LHS = RHS = 360.Hence verified.


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FAQs ~ above LCM the 8, 9, and 10

What is the LCM of 8, 9, and 10?

The LCM that 8, 9, and also 10 is 360. To uncover the least common multiple (LCM) the 8, 9, and also 10, we need to discover the multiples the 8, 9, and also 10 (multiples the 8 = 8, 16, 24, 32 . . . . 360 . . . . ; multiples that 9 = 9, 18, 27, 36 . . . . 360 . . . . ; multiples the 10 = 10, 20, 30, 40 . . . . 360 . . . . ) and also choose the smallest multiple the is precisely divisible through 8, 9, and also 10, i.e., 360.

Which the the following is the LCM that 8, 9, and 10? 52, 10, 42, 360

The worth of LCM of 8, 9, 10 is the smallest common multiple of 8, 9, and 10. The number solve the given problem is 360.

What is the the very least Perfect Square Divisible by 8, 9, and also 10?

The least number divisible by 8, 9, and 10 = LCM(8, 9, 10)LCM of 8, 9, and also 10 = 2 × 2 × 2 × 3 × 3 × 5 ⇒ least perfect square divisible by each 8, 9, and 10 = LCM(8, 9, 10) × 2 × 5 = 3600 Therefore, 3600 is the compelled number.

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What is the Relation between GCF and also LCM that 8, 9, 10?

The following equation deserve to be used to express the relation in between GCF and LCM that 8, 9, 10, i.e. LCM(8, 9, 10) = <(8 × 9 × 10) × GCF(8, 9, 10)>/.