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LCM of 5 and 6

LCM of 5 and 6 is the smallest number among all common multiples of 5 and 6. The first few multiples of 5 and 6 are (5, 10, 15, 20, 25, 30, . . . ) and (6, 12, 18, 24, 30, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 6 - by prime factorization, by division method, and by listing multiples.

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

What is the LCM of 5 and 6?

Answer: LCM of 5 and 6 is 30.

Explanation:

The LCM of two non-zero integers, x(5) and y(6), is the smallest positive integer m(30) that is divisible by both x(5) and y(6) without any remainder.

Methods to Find LCM of 5 and 6

Let's look at the different methods for finding the LCM of 5 and 6.

By Prime Factorization Method
By Division Method
By Listing Multiples

LCM of 5 and 6 by Prime Factorization

Prime factorization of 5 and 6 is (5) = 5¹ and (2 × 3) = 2¹ × 3¹ respectively. LCM of 5 and 6 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ = 30.
Hence, the LCM of 5 and 6 by prime factorization is 30.

LCM of 5 and 6 by Division Method

To calculate the LCM of 5 and 6 by the division method, we will divide the numbers(5, 6) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 6.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 6. Write this prime number(2) on the left of the given numbers(5 and 6), separated as per the ladder arrangement.
Step 2: If any of the given numbers (5, 6) 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 5 and 6 is the product of all prime numbers on the left, i.e. LCM(5, 6) by division method = 2 × 3 × 5 = 30.

LCM of 5 and 6 by Listing Multiples

To calculate the LCM of 5 and 6 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 6 (6, 12, 18, 24, 30, 36, . . . . )
Step 2: The common multiples from the multiples of 5 and 6 are 30, 60, . . .
Step 3: The smallest common multiple of 5 and 6 is 30.

∴ The least common multiple of 5 and 6 = 30.

☛ Also Check:

LCM of 5 and 6 Examples

Example 1: The GCD and LCM of two numbers are 1 and 30 respectively. If one number is 5, find the other number.

Solution:

Let the other number be p.
∵ GCD × LCM = 5 × p
⇒ p = (GCD × LCM)/5
⇒ p = (1 × 30)/5
⇒ p = 6
Therefore, the other number is 6.
Example 2: Verify the relationship between GCF and LCM of 5 and 6.

Solution:

The relation between GCF and LCM of 5 and 6 is given as,
LCM(5, 6) × GCF(5, 6) = Product of 5, 6
Prime factorization of 5 and 6 is given as, 5 = (5) = 5¹ and 6 = (2 × 3) = 2¹ × 3¹
LCM(5, 6) = 30
GCF(5, 6) = 1
LHS = LCM(5, 6) × GCF(5, 6) = 30 × 1 = 30
RHS = Product of 5, 6 = 5 × 6 = 30
⇒ LHS = RHS = 30
Hence, verified.
Example 3: The product of two numbers is 30. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 30
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 30/1
Therefore, the LCM is 30.
The probable combination for the given case is LCM(5, 6) = 30.

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FAQs on LCM of 5 and 6

What is the LCM of 5 and 6?

The LCM of 5 and 6 is 30. To find the least common multiple of 5 and 6, we need to find the multiples of 5 and 6 (multiples of 5 = 5, 10, 15, 20 . . . . 30; multiples of 6 = 6, 12, 18, 24 . . . . 30) and choose the smallest multiple that is exactly divisible by 5 and 6, i.e., 30.

If the LCM of 6 and 5 is 30, Find its GCF.

LCM(6, 5) × GCF(6, 5) = 6 × 5
Since the LCM of 6 and 5 = 30
⇒ 30 × GCF(6, 5) = 30
Therefore, the greatest common factor = 30/30 = 1.

What are the Methods to Find LCM of 5 and 6?

The commonly used methods to find the LCM of 5 and 6 are:

Listing Multiples
Prime Factorization Method
Division Method

What is the Relation Between GCF and LCM of 5, 6?

The following equation can be used to express the relation between GCF and LCM of 5 and 6, i.e. GCF × LCM = 5 × 6.

Which of the following is the LCM of 5 and 6? 3, 32, 35, 30

The value of LCM of 5, 6 is the smallest common multiple of 5 and 6. The number satisfying the given condition is 30.

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