LCM that 3, 4, 5, and also 6 is the smallest number among all common multiples that 3, 4, 5, and also 6. The first couple of multiples the 3, 4, 5, and 6 room (3, 6, 9, 12, 15 . . .), (4, 8, 12, 16, 20 . . .), (5, 10, 15, 20, 25 . . .), and also (6, 12, 18, 24, 30 . . .) respectively. There space 3 typically used approaches to find LCM that 3, 4, 5, 6 - by department method, by element factorization, and by listing multiples.

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

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

Explanation:

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

Let's look in ~ the various methods for finding the LCM the 3, 4, 5, and also 6.

By Listing MultiplesBy element Factorization MethodBy division Method

### LCM that 3, 4, 5, and also 6 through Listing Multiples

To calculate the LCM that 3, 4, 5, 6 by listing out the typical multiples, we can follow the given listed below steps:

Step 1: list 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 common multiples indigenous the multiples that 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 typical multiple of 3, 4, 5, and 6 = 60.

### LCM the 3, 4, 5, and 6 by prime Factorization

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

### LCM of 3, 4, 5, and also 6 by division Method

To calculate the LCM the 3, 4, 5, and 6 by the division method, we will divide the numbers(3, 4, 5, 6) by your prime determinants (preferably common). The product of this divisors offers the LCM the 3, 4, 5, and 6.

Step 2: If any kind of of the offered numbers (3, 4, 5, 6) is a multiple of 2, divide it through 2 and also write the quotient below it. Lug down any kind of number that is no divisible through the element number.Step 3: proceed the measures until just 1s are left in the last row.

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

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

Solution:

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

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

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

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

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

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

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

The least number divisible by 3, 4, 5, and 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 required number.

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### What are the techniques to find LCM that 3, 4, 5, 6?

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