LCM of 4, 7, and 10 is the smallest number amongst all common multiples the 4, 7, and 10. The first couple of multiples that 4, 7, and 10 room (4, 8, 12, 16, 20 . . .), (7, 14, 21, 28, 35 . . .), and also (10, 20, 30, 40, 50 . . .) respectively. There space 3 typically used methods to discover LCM the 4, 7, 10 - by department method, by element factorization, and by listing multiples.

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1.LCM that 4, 7, and also 10
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM the 4, 7, and also 10 is 140.

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Explanation:

The LCM of 3 non-zero integers, a(4), b(7), and c(10), is the smallest positive integer m(140) the is divisible through a(4), b(7), and also c(10) without any kind of remainder.


The methods to find the LCM that 4, 7, and 10 are explained below.

By prime Factorization MethodBy department MethodBy Listing Multiples

LCM of 4, 7, and also 10 by element Factorization

Prime administer of 4, 7, and also 10 is (2 × 2) = 22, (7) = 71, and also (2 × 5) = 21 × 51 respectively. LCM of 4, 7, and 10 can be acquired by multiply prime factors raised to your respective greatest power, i.e. 22 × 51 × 71 = 140.Hence, the LCM of 4, 7, and 10 by prime factorization is 140.

LCM the 4, 7, and also 10 by division Method

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To calculate the LCM the 4, 7, and also 10 by the department method, we will certainly divide the numbers(4, 7, 10) by their prime components (preferably common). The product of these divisors gives the LCM of 4, 7, and also 10.

Step 2: If any kind of of the offered numbers (4, 7, 10) is a lot of of 2, divide it by 2 and write the quotient below it. Bring down any number that is no divisible by the prime number.Step 3: proceed the measures until just 1s are left in the last row.

The LCM the 4, 7, and also 10 is the product of every prime numbers on the left, i.e. LCM(4, 7, 10) by department method = 2 × 2 × 5 × 7 = 140.

LCM that 4, 7, and 10 by Listing Multiples

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To calculate the LCM of 4, 7, 10 by listing out the usual multiples, we have the right to follow the given below steps:

Step 1: list a couple of multiples the 4 (4, 8, 12, 16, 20 . . .), 7 (7, 14, 21, 28, 35 . . .), and 10 (10, 20, 30, 40, 50 . . .).Step 2: The typical multiples indigenous the multiples of 4, 7, and 10 are 140, 280, . . .Step 3: The smallest typical multiple that 4, 7, and also 10 is 140.

∴ The least common multiple of 4, 7, and 10 = 140.

☛ also Check:


Example 1: uncover the smallest number the is divisible by 4, 7, 10 exactly.

Solution:

The value of LCM(4, 7, 10) will certainly be the smallest number the is specifically divisible through 4, 7, and 10.⇒ Multiples the 4, 7, and 10:

Multiples of 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 132, 136, 140, . . . .Multiples the 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 126, 133, 140, . . . .Multiples that 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 100, 110, 120, 130, 140, . . . .

Therefore, the LCM the 4, 7, and also 10 is 140.


Example 2: calculation the LCM the 4, 7, and 10 utilizing the GCD the the given numbers.

Solution:

Prime factorization of 4, 7, 10:

4 = 227 = 7110 = 21 × 51

Therefore, GCD(4, 7) = 1, GCD(7, 10) = 1, GCD(4, 10) = 2, GCD(4, 7, 10) = 1We know,LCM(4, 7, 10) = <(4 × 7 × 10) × GCD(4, 7, 10)>/LCM(4, 7, 10) = (280 × 1)/(1 × 1 × 2) = 140⇒LCM(4, 7, 10) = 140


Example 3: Verify the relationship between the GCD and also LCM the 4, 7, and 10.

Solution:

The relation in between GCD and also LCM of 4, 7, and 10 is given as,LCM(4, 7, 10) = <(4 × 7 × 10) × GCD(4, 7, 10)>/⇒ prime factorization the 4, 7 and 10:

4 = 227 = 7110 = 21 × 51

∴ GCD the (4, 7), (7, 10), (4, 10) and (4, 7, 10) = 1, 1, 2 and also 1 respectively.Now, LHS = LCM(4, 7, 10) = 140.And, RHS = <(4 × 7 × 10) × GCD(4, 7, 10)>/ = <(280) × 1>/<1 × 1 × 2> = 140LHS = RHS = 140.Hence verified.


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FAQs top top LCM that 4, 7, and 10

What is the LCM of 4, 7, and also 10?

The LCM the 4, 7, and 10 is 140. To uncover the LCM (least usual multiple) the 4, 7, and 10, we require to uncover the multiples the 4, 7, and also 10 (multiples the 4 = 4, 8, 12, 16 . . . . 140 . . . . ; multiples of 7 = 7, 14, 21, 28 . . . . 140 . . . . ; multiples that 10 = 10, 20, 30, 40 . . . . 140 . . . . ) and choose the the smallest multiple the is precisely divisible through 4, 7, and also 10, i.e., 140.

What is the Relation in between GCF and also LCM of 4, 7, 10?

The following equation deserve to be used to refer the relation between GCF and also LCM of 4, 7, 10, i.e. LCM(4, 7, 10) = <(4 × 7 × 10) × GCF(4, 7, 10)>/.

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Which of the following is the LCM the 4, 7, and also 10? 3, 21, 10, 140

The value of LCM that 4, 7, 10 is the smallest usual multiple of 4, 7, and 10. The number to solve the given condition is 140.

What space the techniques to find LCM of 4, 7, 10?

The commonly used techniques to find the LCM that 4, 7, 10 are: