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LCM of 5 and 12

LCM of 5 and 12 is the smallest number among all common multiples of 5 and 12. The first few multiples of 5 and 12 are (5, 10, 15, 20, 25, . . . ) and (12, 24, 36, 48, 60, 72, 84, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 12 - by listing multiples, by division method, and by prime factorization.

1.	LCM of 5 and 12
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 5 and 12?

Answer: LCM of 5 and 12 is 60.

Explanation:

The LCM of two non-zero integers, x(5) and y(12), is the smallest positive integer m(60) that is divisible by both x(5) and y(12) without any remainder.

Methods to Find LCM of 5 and 12

The methods to find the LCM of 5 and 12 are explained below.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 5 and 12 by Division Method

To calculate the LCM of 5 and 12 by the division method, we will divide the numbers(5, 12) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 12.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 12. Write this prime number(2) on the left of the given numbers(5 and 12), separated as per the ladder arrangement.
Step 2: If any of the given numbers (5, 12) 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 12 is the product of all prime numbers on the left, i.e. LCM(5, 12) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 5 and 12 by Listing Multiples

To calculate the LCM of 5 and 12 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, . . . ) and 12 (12, 24, 36, 48, 60, 72, 84, . . . . )
Step 2: The common multiples from the multiples of 5 and 12 are 60, 120, . . .
Step 3: The smallest common multiple of 5 and 12 is 60.

∴ The least common multiple of 5 and 12 = 60.

LCM of 5 and 12 by Prime Factorization

Prime factorization of 5 and 12 is (5) = 5¹ and (2 × 2 × 3) = 2² × 3¹ respectively. LCM of 5 and 12 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 5 and 12 by prime factorization is 60.

☛ Also Check:

LCM of 5 and 12 Examples

Example 1: The GCD and LCM of two numbers are 1 and 60 respectively. If one number is 5, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 5 × z
⇒ z = (GCD × LCM)/5
⇒ z = (1 × 60)/5
⇒ z = 12
Therefore, the other number is 12.
Example 2: Verify the relationship between GCF and LCM of 5 and 12.

Solution:

The relation between GCF and LCM of 5 and 12 is given as,
LCM(5, 12) × GCF(5, 12) = Product of 5, 12
Prime factorization of 5 and 12 is given as, 5 = (5) = 5¹ and 12 = (2 × 2 × 3) = 2² × 3¹
LCM(5, 12) = 60
GCF(5, 12) = 1
LHS = LCM(5, 12) × GCF(5, 12) = 60 × 1 = 60
RHS = Product of 5, 12 = 5 × 12 = 60
⇒ LHS = RHS = 60
Hence, verified.
Example 3: The product of two numbers is 60. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 60
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 60/1
Therefore, the LCM is 60.
The probable combination for the given case is LCM(5, 12) = 60.

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FAQs on LCM of 5 and 12

What is the LCM of 5 and 12?

The LCM of 5 and 12 is 60. To find the LCM (least common multiple) of 5 and 12, we need to find the multiples of 5 and 12 (multiples of 5 = 5, 10, 15, 20 . . . . 60; multiples of 12 = 12, 24, 36, 48 . . . . 60) and choose the smallest multiple that is exactly divisible by 5 and 12, i.e., 60.

What is the Least Perfect Square Divisible by 5 and 12?

The least number divisible by 5 and 12 = LCM(5, 12)
LCM of 5 and 12 = 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 5 and 12 = LCM(5, 12) × 3 × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

What is the Relation Between GCF and LCM of 5, 12?

The following equation can be used to express the relation between GCF and LCM of 5 and 12, i.e. GCF × LCM = 5 × 12.

If the LCM of 12 and 5 is 60, Find its GCF.

LCM(12, 5) × GCF(12, 5) = 12 × 5
Since the LCM of 12 and 5 = 60
⇒ 60 × GCF(12, 5) = 60
Therefore, the greatest common factor (GCF) = 60/60 = 1.

What are the Methods to Find LCM of 5 and 12?

The commonly used methods to find the LCM of 5 and 12 are:

Listing Multiples
Division Method
Prime Factorization Method

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