LCM that 2, 3, and also 5 is the the smallest number amongst all typical multiples the 2, 3, and 5. The first couple of multiples of 2, 3, and also 5 room (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and also (5, 10, 15, 20, 25 . . .) respectively. There are 3 commonly used methods to find LCM of 2, 3, 5 - by listing multiples, by prime factorization, and also by division method.

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1. | LCM the 2, 3, and also 5 |

2. | List of Methods |

3. | Solved Examples |

4. | FAQs |

**Answer:** LCM that 2, 3, and also 5 is 30.

**Explanation: **

The LCM of 3 non-zero integers, a(2), b(3), and also c(5), is the smallest optimistic integer m(30) the is divisible by a(2), b(3), and also c(5) without any kind of remainder.

Let's look in ~ the various methods for finding the LCM the 2, 3, and 5.

By element Factorization MethodBy department MethodBy Listing Multiples### LCM the 2, 3, and also 5 by prime Factorization

Prime administer of 2, 3, and also 5 is (2) = 21, (3) = 31, and (5) = 51 respectively. LCM that 2, 3, and 5 have the right to be derived by multiply prime factors raised to your respective highest possible power, i.e. 21 × 31 × 51 = 30.Hence, the LCM that 2, 3, and 5 by element factorization is 30.

### LCM that 2, 3, and also 5 by department Method

To calculate the LCM the 2, 3, and also 5 by the department method, we will divide the numbers(2, 3, 5) by your prime factors (preferably common). The product of this divisors provides the LCM the 2, 3, and also 5.

**Step 2:**If any of the provided numbers (2, 3, 5) is a multiple of 2, divide it by 2 and also write the quotient below it. Lug down any number the is no divisible through the element number.

**Step 3:**proceed the procedures until only 1s are left in the last row.

The LCM that 2, 3, and also 5 is the product of all prime number on the left, i.e. LCM(2, 3, 5) by department method = 2 × 3 × 5 = 30.

### LCM the 2, 3, and 5 by Listing Multiples

To calculation the LCM the 2, 3, 5 by listing out the usual multiples, we have the right to follow the given listed below steps:

**Step 1:**list a few multiples of 2 (2, 4, 6, 8, 10 . . .), 3 (3, 6, 9, 12, 15 . . .), and 5 (5, 10, 15, 20, 25 . . .).

**Step 2:**The typical multiples native the multiples that 2, 3, and also 5 are 30, 60, . . .

**Step 3:**The smallest common multiple the 2, 3, and 5 is 30.

∴ The least typical multiple the 2, 3, and also 5 = 30.

**☛ additionally Check:**

**Example 2: Verify the relationship between the GCD and LCM that 2, 3, and 5.**

**Solution:**

The relation in between GCD and LCM of 2, 3, and also 5 is provided as,LCM(2, 3, 5) = <(2 × 3 × 5) × GCD(2, 3, 5)>/

∴ GCD of (2, 3), (3, 5), (2, 5) and (2, 3, 5) = 1, 1, 1 and 1 respectively.Now, LHS = LCM(2, 3, 5) = 30.And, RHS = <(2 × 3 × 5) × GCD(2, 3, 5)>/

**Example 3: discover the smallest number that is divisible through 2, 3, 5 exactly. **

**Solution: **

The smallest number that is divisible by 2, 3, and 5 specifically is their LCM.⇒ Multiples the 2, 3, and 5:

**Multiples the 2**= 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, . . . .

**Multiples the 3**= 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . .

**Multiples the 5**= 5, 10, 15, 20, 25, 30, 35, . . . .

Therefore, the LCM that 2, 3, and also 5 is 30.

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## FAQs top top LCM that 2, 3, and also 5

### What is the LCM the 2, 3, and also 5?

The **LCM of 2, 3, and also 5 is 30**. To uncover the LCM the 2, 3, and 5, we require to find the multiples of 2, 3, and also 5 (multiples that 2 = 2, 4, 6, 8 . . . . 30 . . . . ; multiples of 3 = 3, 6, 9, 12 . . . . 30 . . . . ; multiples that 5 = 5, 10, 15, 20, 30 . . . .) and choose the the smallest multiple that is precisely divisible by 2, 3, and also 5, i.e., 30.

### Which the the following is the LCM the 2, 3, and also 5? 3, 30, 81, 24

The worth of LCM the 2, 3, 5 is the smallest common multiple of 2, 3, and 5. The number solve the given problem is 30.

### How to uncover the LCM that 2, 3, and also 5 by prime Factorization?

To find the LCM of 2, 3, and also 5 making use of prime factorization, us will discover the prime factors, (2 = 21), (3 = 31), and also (5 = 51). LCM of 2, 3, and also 5 is the product of prime determinants raised to your respective highest exponent among the number 2, 3, and 5.⇒ LCM of 2, 3, 5 = 21 × 31 × 51 = 30.

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### What is the the very least Perfect Square Divisible by 2, 3, and 5?

The the very least number divisible through 2, 3, and also 5 = LCM(2, 3, 5)LCM of 2, 3, and 5 = 2 × 3 × 5