LCM the 3, 7, and also 10 is the the smallest number amongst all typical multiples of 3, 7, and 10. The first few multiples that 3, 7, and 10 space (3, 6, 9, 12, 15 . . .), (7, 14, 21, 28, 35 . . .), and (10, 20, 30, 40, 50 . . .) respectively. There space 3 frequently used techniques to uncover LCM of 3, 7, 10 - by element factorization, by listing multiples, and by department method.

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1.LCM of 3, 7, and 10
2.List the Methods
3.Solved Examples
4.FAQs

Answer: LCM that 3, 7, and 10 is 210.

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Explanation:

The LCM of three non-zero integers, a(3), b(7), and also c(10), is the smallest optimistic integer m(210) that is divisible by a(3), b(7), and c(10) without any remainder.


Let's look at the various methods for finding the LCM of 3, 7, and also 10.

By element Factorization MethodBy department MethodBy Listing Multiples

LCM that 3, 7, and also 10 by element Factorization

Prime factorization of 3, 7, and 10 is (3) = 31, (7) = 71, and also (2 × 5) = 21 × 51 respectively. LCM that 3, 7, and also 10 can be obtained by multiplying prime factors raised to your respective highest possible power, i.e. 21 × 31 × 51 × 71 = 210.Hence, the LCM of 3, 7, and 10 by element factorization is 210.

LCM of 3, 7, and also 10 by department Method

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To calculation the LCM of 3, 7, and 10 through the department method, we will certainly divide the numbers(3, 7, 10) by their prime factors (preferably common). The product of these divisors provides the LCM that 3, 7, and also 10.

Step 2: If any of the provided numbers (3, 7, 10) is a lot of of 2, divide it through 2 and write the quotient listed below it. Bring down any kind of number the is no divisible by the element number.Step 3: continue the measures until only 1s are left in the last row.

The LCM of 3, 7, and also 10 is the product of every prime number on the left, i.e. LCM(3, 7, 10) by department method = 2 × 3 × 5 × 7 = 210.

LCM that 3, 7, and 10 by Listing Multiples

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To calculation the LCM of 3, 7, 10 through listing out the usual multiples, we deserve to follow the given below steps:

Step 1: perform a few multiples that 3 (3, 6, 9, 12, 15 . . .), 7 (7, 14, 21, 28, 35 . . .), and also 10 (10, 20, 30, 40, 50 . . .).Step 2: The usual multiples native the multiples of 3, 7, and 10 room 210, 420, . . .Step 3: The smallest usual multiple of 3, 7, and also 10 is 210.

∴ The least typical multiple the 3, 7, and 10 = 210.

☛ likewise Check:


Example 2: discover the smallest number that is divisible by 3, 7, 10 exactly.

Solution:

The value of LCM(3, 7, 10) will be the smallest number that is specifically divisible by 3, 7, and 10.⇒ Multiples that 3, 7, and also 10:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 204, 207, 210, . . . .Multiples that 7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, . . . ., 182, 189, 196, 203, 210, . . . .Multiples that 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 180, 190, 200, 210, . . . .

Therefore, the LCM that 3, 7, and 10 is 210.


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

Solution:

The relation between GCD and also LCM that 3, 7, and 10 is offered as,LCM(3, 7, 10) = <(3 × 7 × 10) × GCD(3, 7, 10)>/⇒ prime factorization the 3, 7 and also 10:

3 = 317 = 7110 = 21 × 51

∴ GCD of (3, 7), (7, 10), (3, 10) and (3, 7, 10) = 1, 1, 1 and 1 respectively.Now, LHS = LCM(3, 7, 10) = 210.And, RHS = <(3 × 7 × 10) × GCD(3, 7, 10)>/ = <(210) × 1>/<1 × 1 × 1> = 210LHS = RHS = 210.Hence verified.


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FAQs ~ above LCM that 3, 7, and 10

What is the LCM of 3, 7, and 10?

The LCM that 3, 7, and also 10 is 210. To discover the LCM (least typical multiple) the 3, 7, and also 10, we need to discover the multiples of 3, 7, and also 10 (multiples the 3 = 3, 6, 9, 12 . . . . 210 . . . . ; multiples that 7 = 7, 14, 21, 28 . . . . 210 . . . . ; multiples the 10 = 10, 20, 30, 40 . . . . 210 . . . . ) and also choose the smallest multiple that is precisely divisible through 3, 7, and also 10, i.e., 210.

Which the the adhering to is the LCM the 3, 7, and also 10? 81, 30, 210, 15

The value of LCM of 3, 7, 10 is the smallest typical multiple the 3, 7, and also 10. The number to solve the given problem is 210.

How to discover the LCM that 3, 7, and 10 by element Factorization?

To uncover the LCM of 3, 7, and also 10 utilizing prime factorization, us will discover the prime factors, (3 = 31), (7 = 71), and (10 = 21 × 51). LCM the 3, 7, and also 10 is the product of prime determinants raised to your respective highest exponent amongst the numbers 3, 7, and 10.⇒ LCM the 3, 7, 10 = 21 × 31 × 51 × 71 = 210.

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What is the least Perfect Square Divisible by 3, 7, and 10?

The least number divisible by 3, 7, and 10 = LCM(3, 7, 10)LCM the 3, 7, and 10 = 2 × 3 × 5 × 7 ⇒ least perfect square divisible by each 3, 7, and also 10 = LCM(3, 7, 10) × 2 × 3 × 5 × 7 = 44100 Therefore, 44100 is the forced number.