LCM that 3, 4, 5, and 6 is the smallest number among all usual multiples that 3, 4, 5, and 6. The first few multiples the 3, 4, 5, and 6 are (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), and (6, 12, 18, 24, 30 . . .) respectively. There space 3 frequently used techniques to uncover LCM of 3, 4, 5, 6 - by division method, by prime factorization, and also by listing multiples.

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1.LCM the 3, 4, 5, and 6
2.List that Methods
3.Solved Examples
4.FAQs

Answer: LCM that 3, 4, 5, and also 6 is 60.

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Explanation:

The LCM of four non-zero integers, a(3), b(4), c(5), and also d(6), is the smallest optimistic integer m(60) that is divisible through a(3), b(4), c(5), and also d(6) without any type of remainder.


Let's look at the various methods because that finding the LCM of 3, 4, 5, and 6.

By Listing MultiplesBy prime Factorization MethodBy division Method

LCM the 3, 4, 5, and also 6 by Listing Multiples

To calculation the LCM the 3, 4, 5, 6 through listing out the typical multiples, we can follow the given below steps:

Step 1: perform a couple of multiples the 3 (3, 6, 9, 12, 15 . . .), 4 (4, 8, 12, 16, 20 . . .), 5 (5, 10, 15, 20, 25 . . .), and also 6 (6, 12, 18, 24, 30 . . .).Step 2: The typical multiples from the multiples of 3, 4, 5, and also 6 space 60, 120, . . .Step 3: The smallest typical multiple the 3, 4, 5, and also 6 is 60.

∴ The least usual multiple of 3, 4, 5, and 6 = 60.

LCM that 3, 4, 5, and also 6 by prime Factorization

Prime administrate of 3, 4, 5, and also 6 is (3) = 31, (2 × 2) = 22, (5) = 51, and also (2 × 3) = 21 × 31 respectively. LCM the 3, 4, 5, and also 6 can be acquired by multiply prime determinants raised to their respective highest power, i.e. 22 × 31 × 51 = 60.Hence, the LCM that 3, 4, 5, and also 6 by element factorization is 60.

LCM the 3, 4, 5, and 6 by division Method

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To calculation the LCM the 3, 4, 5, and 6 by the division method, we will certainly divide the numbers(3, 4, 5, 6) by their prime determinants (preferably common). The product of this divisors provides the LCM of 3, 4, 5, and also 6.

Step 2: If any of the given numbers (3, 4, 5, 6) is a many of 2, division it by 2 and also write the quotient below it. Carry down any type of number that is not divisible by the prime number.Step 3: continue the steps until just 1s are left in the last row.

The LCM the 3, 4, 5, and 6 is the product of every prime numbers on the left, i.e. LCM(3, 4, 5, 6) by department method = 2 × 2 × 3 × 5 = 60.

☛ also Check:


Example 3: discover the smallest number the is divisible through 3, 4, 5, 6 exactly.

Solution:

The worth of LCM(3, 4, 5, 6) will be the the smallest number that is exactly divisible by 3, 4, 5, and also 6.⇒ Multiples that 3, 4, 5, and 6:

Multiples the 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .Multiples that 4 = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, . . . ., 52, 56, 60, . . . .Multiples that 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .Multiples the 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . ., 42, 48, 54, 60, . . . .

Therefore, the LCM the 3, 4, 5, and 6 is 60.


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FAQs on LCM the 3, 4, 5, and also 6

What is the LCM that 3, 4, 5, and also 6?

The LCM of 3, 4, 5, and 6 is 60. To uncover the LCM (least typical multiple) that 3, 4, 5, and 6, we need to discover the multiples that 3, 4, 5, and also 6 (multiples of 3 = 3, 6, 9, 12 . . . . 60 . . . . ; multiples that 4 = 4, 8, 12, 16 . . . . 60 . . . . ; multiples the 5 = 5, 10, 15, 20 . . . . 60 . . . . ; multiples the 6 = 6, 12, 18, 24 . . . . 60 . . . . ) and also choose the the smallest multiple that is specifically divisible by 3, 4, 5, and also 6, i.e., 60.

What is the the very least Perfect Square Divisible by 3, 4, 5, and also 6?

The the very least number divisible through 3, 4, 5, and also 6 = LCM(3, 4, 5, 6)LCM the 3, 4, 5, and also 6 = 2 × 2 × 3 × 5 ⇒ least perfect square divisible by every 3, 4, 5, and also 6 = LCM(3, 4, 5, 6) × 3 × 5 = 900 Therefore, 900 is the compelled number.

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What are the techniques to discover LCM the 3, 4, 5, 6?

The generally used approaches to discover the LCM the 3, 4, 5, 6 are:

Division MethodListing MultiplesPrime administrate Method

Which of the complying with is the LCM of 3, 4, 5, and also 6? 60, 3, 52, 12

The worth of LCM that 3, 4, 5, 6 is the smallest typical multiple that 3, 4, 5, and 6. The number satisfying the given condition is 60.