LCM that 8, 10, and 15 is the the smallest number among all typical multiples the 8, 10, and also 15. The first couple of multiples of 8, 10, and 15 space (8, 16, 24, 32, 40 . . .), (10, 20, 30, 40, 50 . . .), and (15, 30, 45, 60, 75 . . .) respectively. There space 3 typically used methods to uncover LCM of 8, 10, 15 - through listing multiples, by department method, and also by element factorization.

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1.LCM that 8, 10, and also 15
2.List of Methods
3.Solved Examples
4.FAQs

Answer: LCM that 8, 10, and 15 is 120.

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Explanation:

The LCM of 3 non-zero integers, a(8), b(10), and also c(15), is the smallest confident integer m(120) the is divisible through a(8), b(10), and c(15) without any remainder.


Let's look at the various methods because that finding the LCM the 8, 10, and 15.

By Listing MultiplesBy department MethodBy prime Factorization Method

LCM that 8, 10, and 15 by Listing Multiples

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To calculate the LCM the 8, 10, 15 by listing the end the typical multiples, we deserve to follow the given below steps:

Step 1: list a few multiples that 8 (8, 16, 24, 32, 40 . . .), 10 (10, 20, 30, 40, 50 . . .), and also 15 (15, 30, 45, 60, 75 . . .).Step 2: The typical multiples indigenous the multiples of 8, 10, and 15 space 120, 240, . . .Step 3: The smallest common multiple of 8, 10, and also 15 is 120.

∴ The least usual multiple the 8, 10, and also 15 = 120.

LCM of 8, 10, and 15 by division Method

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To calculate the LCM that 8, 10, and 15 through the division method, we will divide the numbers(8, 10, 15) by their prime components (preferably common). The product of this divisors provides the LCM the 8, 10, and also 15.

Step 2: If any of the offered numbers (8, 10, 15) is a lot of of 2, division it by 2 and write the quotient below it. Bring down any kind of number that is not divisible by the prime number.Step 3: continue the measures until only 1s room left in the critical row.

The LCM the 8, 10, and 15 is the product of every prime number on the left, i.e. LCM(8, 10, 15) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 8, 10, and 15 by prime Factorization

Prime administer of 8, 10, and also 15 is (2 × 2 × 2) = 23, (2 × 5) = 21 × 51, and (3 × 5) = 31 × 51 respectively. LCM that 8, 10, and 15 can be obtained by multiply prime factors raised to your respective greatest power, i.e. 23 × 31 × 51 = 120.Hence, the LCM that 8, 10, and also 15 by prime factorization is 120.

☛ likewise Check:


Example 3: Verify the relationship between the GCD and also LCM the 8, 10, and also 15.

Solution:

The relation between GCD and LCM the 8, 10, and 15 is given as,LCM(8, 10, 15) = <(8 × 10 × 15) × GCD(8, 10, 15)>/⇒ prime factorization that 8, 10 and also 15:

8 = 2310 = 21 × 5115 = 31 × 51

∴ GCD that (8, 10), (10, 15), (8, 15) and also (8, 10, 15) = 2, 5, 1 and 1 respectively.Now, LHS = LCM(8, 10, 15) = 120.And, RHS = <(8 × 10 × 15) × GCD(8, 10, 15)>/ = <(1200) × 1>/<2 × 5 × 1> = 120LHS = RHS = 120.Hence verified.


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FAQs on LCM that 8, 10, and also 15

What is the LCM that 8, 10, and 15?

The LCM of 8, 10, and also 15 is 120. To uncover the least usual multiple (LCM) that 8, 10, and also 15, we need to discover the multiples of 8, 10, and 15 (multiples of 8 = 8, 16, 24, 32 . . . . 120 . . . . ; multiples of 10 = 10, 20, 30, 40 . . . . 120 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . . 120 . . . . ) and also choose the the smallest multiple that is exactly divisible by 8, 10, and also 15, i.e., 120.

What room the approaches to discover LCM the 8, 10, 15?

The commonly used techniques to uncover the LCM of 8, 10, 15 are:

Prime administrate MethodDivision MethodListing Multiples

Which the the adhering to is the LCM of 8, 10, and also 15? 25, 100, 120, 81

The value of LCM the 8, 10, 15 is the smallest common multiple the 8, 10, and 15. The number solve the given condition is 120.

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What is the the very least Perfect Square Divisible through 8, 10, and 15?

The the very least number divisible by 8, 10, and 15 = LCM(8, 10, 15)LCM of 8, 10, and 15 = 2 × 2 × 2 × 3 × 5 ⇒ least perfect square divisible by every 8, 10, and 15 = LCM(8, 10, 15) × 2 × 3 × 5 = 3600 Therefore, 3600 is the forced number.