LCM of 2, 3, and 5 is the smallest number among all common multiples of 2, 3, and 5. The first few multiples of 2, 3, and 5 are (2, 4, 6, 8, 10 . . .), (3, 6, 9, 12, 15 . . .), and (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 by division method.

You are watching: What is the lcm of 2 3 and 5

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

Answer: LCM of 2, 3, and 5 is 30.

*

Explanation:

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


Let's look at the different methods for finding the LCM of 2, 3, and 5.

By Prime Factorization MethodBy Division MethodBy Listing Multiples

LCM of 2, 3, and 5 by Prime Factorization

Prime factorization of 2, 3, and 5 is (2) = 21, (3) = 31, and (5) = 51 respectively. LCM of 2, 3, and 5 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 21 × 31 × 51 = 30.Hence, the LCM of 2, 3, and 5 by prime factorization is 30.

LCM of 2, 3, and 5 by Division Method

*

To calculate the LCM of 2, 3, and 5 by the division method, we will divide the numbers(2, 3, 5) by their prime factors (preferably common). The product of these divisors gives the LCM of 2, 3, and 5.

Step 2: If any of the given numbers (2, 3, 5) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.Step 3: Continue the steps until only 1s are left in the last row.

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

LCM of 2, 3, and 5 by Listing Multiples

*

To calculate the LCM of 2, 3, 5 by listing out the common multiples, we can follow the given 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 common multiples from the multiples of 2, 3, and 5 are 30, 60, . . .Step 3: The smallest common multiple of 2, 3, and 5 is 30.

∴ The least common multiple of 2, 3, and 5 = 30.

☛ Also Check:


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

Solution:

The relation between GCD and LCM of 2, 3, and 5 is given as,LCM(2, 3, 5) = <(2 × 3 × 5) × GCD(2, 3, 5)>/⇒ Prime factorization of 2, 3 and 5:

2 = 213 = 315 = 51

∴ 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)>/ = <(30) × 1>/<1 × 1 × 1> = 30LHS = RHS = 30.Hence verified.


Example 3: Find the smallest number that is divisible by 2, 3, 5 exactly.

Solution:

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

Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, . . . .Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . .Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, . . . .

Therefore, the LCM of 2, 3, and 5 is 30.


Show Solution >

go to slidego to slidego to slide


*


FAQs on LCM of 2, 3, and 5

What is the LCM of 2, 3, and 5?

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

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

The value of LCM of 2, 3, 5 is the smallest common multiple of 2, 3, and 5. The number satisfying the given condition is 30.

How to Find the LCM of 2, 3, and 5 by Prime Factorization?

To find the LCM of 2, 3, and 5 using prime factorization, we will find the prime factors, (2 = 21), (3 = 31), and (5 = 51). LCM of 2, 3, and 5 is the product of prime factors raised to their respective highest exponent among the numbers 2, 3, and 5.⇒ LCM of 2, 3, 5 = 21 × 31 × 51 = 30.

See more: Three Points That Are Coplanar But Not Collinear And Coplanar Points?

What is the Least Perfect Square Divisible by 2, 3, and 5?

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