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

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 1 LCM that 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.

Explanation:

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

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

By Listing MultiplesBy prime Factorization MethodBy department Method

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

To calculation the LCM of 3, 4, 5, 6 by listing the end the common multiples, we have the right to follow the given below steps:

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

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

### LCM of 3, 4, 5, and also 6 by prime Factorization

Prime administer of 3, 4, 5, and 6 is (3) = 31, (2 × 2) = 22, (5) = 51, and (2 × 3) = 21 × 31 respectively. LCM the 3, 4, 5, and 6 can be acquired by multiplying prime factors raised to your respective highest possible power, i.e. 22 × 31 × 51 = 60.Hence, the LCM of 3, 4, 5, and also 6 by prime factorization is 60.

### LCM the 3, 4, 5, and 6 by department Method

To calculation the LCM that 3, 4, 5, and 6 by the department method, we will divide the numbers(3, 4, 5, 6) by their prime components (preferably common). The product of these divisors offers the LCM of 3, 4, 5, and 6.

Step 2: If any of the offered numbers (3, 4, 5, 6) is a many of 2, division it by 2 and write the quotient listed below it. Bring down any number that is no divisible by the element number.Step 3: proceed the measures until only 1s room left in the critical row.

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

☛ also Check:

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

Solution:

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

Multiples that 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 48, 51, 54, 57, 60, . . . .Multiples of 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 of 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.

## FAQs top top LCM that 3, 4, 5, and 6

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

The LCM of 3, 4, 5, and also 6 is 60. To find the LCM (least typical multiple) of 3, 4, 5, and also 6, we need to uncover 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 of 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 6, i.e., 60.

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

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

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### What space the approaches to discover LCM the 3, 4, 5, 6?

The commonly used approaches to find the LCM of 3, 4, 5, 6 are: