LCM the 10, 15, and also 25 is the smallest number among all usual multiples that 10, 15, and 25. The first couple of multiples that 10, 15, and also 25 space (10, 20, 30, 40, 50 . . .), (15, 30, 45, 60, 75 . . .), and also (25, 50, 75, 100, 125 . . .) respectively. There room 3 generally used techniques to find LCM the 10, 15, 25 - by element factorization, by department method, and also by listing multiples.

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1.LCM of 10, 15, and also 25
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM that 10, 15, and also 25 is 150.

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Explanation:

The LCM of three non-zero integers, a(10), b(15), and also c(25), is the smallest optimistic integer m(150) that is divisible by a(10), b(15), and also c(25) without any kind of remainder.


The approaches to discover the LCM the 10, 15, and also 25 are defined below.

By element Factorization MethodBy Listing MultiplesBy division Method

LCM that 10, 15, and also 25 by prime Factorization

Prime administrate of 10, 15, and 25 is (2 × 5) = 21 × 51, (3 × 5) = 31 × 51, and also (5 × 5) = 52 respectively. LCM of 10, 15, and 25 have the right to be acquired by multiplying prime determinants raised to your respective highest power, i.e. 21 × 31 × 52 = 150.Hence, the LCM the 10, 15, and 25 by prime factorization is 150.

LCM the 10, 15, and also 25 by Listing Multiples

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To calculation the LCM that 10, 15, 25 by listing out the usual multiples, we deserve to follow the given listed below steps:

Step 1: list a couple of multiples of 10 (10, 20, 30, 40, 50 . . .), 15 (15, 30, 45, 60, 75 . . .), and 25 (25, 50, 75, 100, 125 . . .).Step 2: The common multiples from the multiples the 10, 15, and also 25 are 150, 300, . . .Step 3: The smallest common multiple the 10, 15, and also 25 is 150.

∴ The least typical multiple the 10, 15, and also 25 = 150.

LCM the 10, 15, and 25 by division Method

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To calculation the LCM that 10, 15, and 25 by the department method, we will divide the numbers(10, 15, 25) by your prime determinants (preferably common). The product of this divisors offers the LCM that 10, 15, and 25.

Step 2: If any kind of of the provided numbers (10, 15, 25) is a multiple of 2, division it by 2 and also write the quotient below it. Bring down any kind of number the is no divisible by the prime number.Step 3: proceed the measures until just 1s space left in the last row.

The LCM that 10, 15, and 25 is the product of every prime number on the left, i.e. LCM(10, 15, 25) by division method = 2 × 3 × 5 × 5 = 150.

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Example 2: Verify the relationship between the GCD and also LCM the 10, 15, and also 25.

Solution:

The relation in between GCD and LCM of 10, 15, and also 25 is given as,LCM(10, 15, 25) = <(10 × 15 × 25) × GCD(10, 15, 25)>/⇒ element factorization of 10, 15 and also 25:

10 = 21 × 5115 = 31 × 5125 = 52

∴ GCD of (10, 15), (15, 25), (10, 25) and (10, 15, 25) = 5, 5, 5 and 5 respectively.Now, LHS = LCM(10, 15, 25) = 150.And, RHS = <(10 × 15 × 25) × GCD(10, 15, 25)>/ = <(3750) × 5>/<5 × 5 × 5> = 150LHS = RHS = 150.Hence verified.


Example 3: calculate the LCM the 10, 15, and also 25 using the GCD the the offered numbers.

Solution:

Prime administrate of 10, 15, 25:

10 = 21 × 5115 = 31 × 5125 = 52

Therefore, GCD(10, 15) = 5, GCD(15, 25) = 5, GCD(10, 25) = 5, GCD(10, 15, 25) = 5We know,LCM(10, 15, 25) = <(10 × 15 × 25) × GCD(10, 15, 25)>/LCM(10, 15, 25) = (3750 × 5)/(5 × 5 × 5) = 150⇒LCM(10, 15, 25) = 150


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FAQs top top LCM the 10, 15, and 25

What is the LCM that 10, 15, and also 25?

The LCM that 10, 15, and also 25 is 150. To discover the least common multiple (LCM) the 10, 15, and 25, we require to find the multiples of 10, 15, and 25 (multiples that 10 = 10, 20, 30, 40 . . . . 150 . . . . ; multiples of 15 = 15, 30, 45, 60 . . . . 150 . . . . ; multiples the 25 = 25, 50, 75, 100, 150 . . . .) and choose the the smallest multiple the is precisely divisible by 10, 15, and 25, i.e., 150.

Which the the adhering to is the LCM that 10, 15, and also 25? 25, 150, 35, 10

The worth of LCM of 10, 15, 25 is the smallest typical multiple the 10, 15, and also 25. The number to solve the given condition is 150.

How to uncover the LCM the 10, 15, and 25 by prime Factorization?

To discover the LCM that 10, 15, and also 25 making use of prime factorization, we will discover the prime factors, (10 = 21 × 51), (15 = 31 × 51), and (25 = 52). LCM of 10, 15, and also 25 is the product the prime factors raised to your respective highest exponent amongst the numbers 10, 15, and also 25.⇒ LCM that 10, 15, 25 = 21 × 31 × 52 = 150.

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What is the least Perfect Square Divisible through 10, 15, and also 25?

The least number divisible through 10, 15, and 25 = LCM(10, 15, 25)LCM that 10, 15, and 25 = 2 × 3 × 5 × 5 ⇒ least perfect square divisible by every 10, 15, and 25 = LCM(10, 15, 25) × 2 × 3 = 900 Therefore, 900 is the required number.