LCM of 3, 4, 5, and also 6 is the the smallest number among all usual multiples that 3, 4, 5, and also 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 generally used methods to uncover LCM the 3, 4, 5, 6 - by department method, by prime factorization, and by listing multiples.

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 1 LCM of 3, 4, 5, and 6 2 List of Methods 3 Solved Examples 4 FAQs

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

Explanation:

The LCM of 4 non-zero integers, a(3), b(4), c(5), and also d(6), is the smallest positive integer m(60) that is divisible by 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 department Method

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

To calculation the LCM of 3, 4, 5, 6 by listing the end the usual multiples, we can follow the given listed below steps:

Step 1: perform a couple of multiples that 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 usual multiples native the multiples of 3, 4, 5, and 6 room 60, 120, . . .Step 3: The smallest common multiple of 3, 4, 5, and also 6 is 60.

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

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

Prime administrate of 3, 4, 5, and 6 is (3) = 31, (2 × 2) = 22, (5) = 51, and also (2 × 3) = 21 × 31 respectively. LCM that 3, 4, 5, and 6 deserve to be obtained by multiplying prime components raised to your 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 of 3, 4, 5, and also 6 by department Method

To calculation the LCM that 3, 4, 5, and also 6 by the division method, we will divide the numbers(3, 4, 5, 6) by their prime factors (preferably common). The product of this divisors provides the LCM that 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. Bring down any number the is not divisible by the element number.Step 3: proceed the measures until just 1s room left in the critical row.

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

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

Solution:

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

Multiples of 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 the 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 of 3, 4, 5, and also 6 is 60.

FAQs on LCM of 3, 4, 5, and 6

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

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

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

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

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What space the methods to uncover LCM of 3, 4, 5, 6?

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

Division MethodListing MultiplesPrime factorization Method

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

The value of LCM that 3, 4, 5, 6 is the smallest usual multiple of 3, 4, 5, and 6. The number to solve the given problem is 60.