A day full of math games & activities. Find one near you.

LCM of 4 and 5

LCM of 4 and 5 is the smallest number among all common multiples of 4 and 5. The first few multiples of 4 and 5 are (4, 8, 12, 16, . . . ) and (5, 10, 15, 20, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 5 - by division method, by prime factorization, and by listing multiples.

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

What is the LCM of 4 and 5?

Answer: LCM of 4 and 5 is 20.

Explanation:

The LCM of two non-zero integers, x(4) and y(5), is the smallest positive integer m(20) that is divisible by both x(4) and y(5) without any remainder.

Methods to Find LCM of 4 and 5

Let's look at the different methods for finding the LCM of 4 and 5.

By Division Method
By Listing Multiples
By Prime Factorization Method

LCM of 4 and 5 by Division Method

To calculate the LCM of 4 and 5 by the division method, we will divide the numbers(4, 5) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 5.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 5. Write this prime number(2) on the left of the given numbers(4 and 5), separated as per the ladder arrangement.
Step 2: If any of the given numbers (4, 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 4 and 5 is the product of all prime numbers on the left, i.e. LCM(4, 5) by division method = 2 × 2 × 5 = 20.

LCM of 4 and 5 by Listing Multiples

To calculate the LCM of 4 and 5 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 4 (4, 8, 12, 16, . . . ) and 5 (5, 10, 15, 20, . . . . )
Step 2: The common multiples from the multiples of 4 and 5 are 20, 40, . . .
Step 3: The smallest common multiple of 4 and 5 is 20.

∴ The least common multiple of 4 and 5 = 20.

LCM of 4 and 5 by Prime Factorization

Prime factorization of 4 and 5 is (2 × 2) = 2² and (5) = 5¹ respectively. LCM of 4 and 5 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5¹ = 20.
Hence, the LCM of 4 and 5 by prime factorization is 20.

☛ Also Check:

LCM of 4 and 5 Examples

Example 1: Verify the relationship between GCF and LCM of 4 and 5.

Solution:

The relation between GCF and LCM of 4 and 5 is given as,
LCM(4, 5) × GCF(4, 5) = Product of 4, 5
Prime factorization of 4 and 5 is given as, 4 = (2 × 2) = 2² and 5 = (5) = 5¹
LCM(4, 5) = 20
GCF(4, 5) = 1
LHS = LCM(4, 5) × GCF(4, 5) = 20 × 1 = 20
RHS = Product of 4, 5 = 4 × 5 = 20
⇒ LHS = RHS = 20
Hence, verified.
Example 2: The GCD and LCM of two numbers are 1 and 20 respectively. If one number is 4, find the other number.

Solution:

Let the other number be z.
∵ GCD × LCM = 4 × z
⇒ z = (GCD × LCM)/4
⇒ z = (1 × 20)/4
⇒ z = 5
Therefore, the other number is 5.
Example 3: The product of two numbers is 20. If their GCD is 1, what is their LCM?

Solution:

Given: GCD = 1
product of numbers = 20
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 20/1
Therefore, the LCM is 20.
The probable combination for the given case is LCM(4, 5) = 20.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on LCM of 4 and 5

What is the LCM of 4 and 5?

The LCM of 4 and 5 is 20. To find the LCM of 4 and 5, we need to find the multiples of 4 and 5 (multiples of 4 = 4, 8, 12, 16 . . . . 20; multiples of 5 = 5, 10, 15, 20) and choose the smallest multiple that is exactly divisible by 4 and 5, i.e., 20.

How to Find the LCM of 4 and 5 by Prime Factorization?

To find the LCM of 4 and 5 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (5 = 5). LCM of 4 and 5 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 5.
⇒ LCM of 4, 5 = 2² × 5¹ = 20.

What is the Least Perfect Square Divisible by 4 and 5?

The least number divisible by 4 and 5 = LCM(4, 5)
LCM of 4 and 5 = 2 × 2 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 4 and 5 = LCM(4, 5) × 5 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.

If the LCM of 5 and 4 is 20, Find its GCF.

LCM(5, 4) × GCF(5, 4) = 5 × 4
Since the LCM of 5 and 4 = 20
⇒ 20 × GCF(5, 4) = 20
Therefore, the GCF (greatest common factor) = 20/20 = 1.

Which of the following is the LCM of 4 and 5? 5, 21, 45, 20

The value of LCM of 4, 5 is the smallest common multiple of 4 and 5. The number satisfying the given condition is 20.

Download FREE Study Materials

LCM and GCF

Math worksheets and
visual curriculum