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LCM of 4 and 20

LCM of 4 and 20 is the smallest number among all common multiples of 4 and 20. The first few multiples of 4 and 20 are (4, 8, 12, 16, 20, . . . ) and (20, 40, 60, 80, 100, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 20 - by division method, by prime factorization, and by listing multiples.

1.	LCM of 4 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 4 and 20?

Answer: LCM of 4 and 20 is 20.

Explanation:

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

Methods to Find LCM of 4 and 20

The methods to find the LCM of 4 and 20 are explained below.

By Listing Multiples
By Division Method
By Prime Factorization Method

LCM of 4 and 20 by Listing Multiples

To calculate the LCM of 4 and 20 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, 20, . . . ) and 20 (20, 40, 60, 80, 100, 120, . . . . )
Step 2: The common multiples from the multiples of 4 and 20 are 20, 40, . . .
Step 3: The smallest common multiple of 4 and 20 is 20.

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

LCM of 4 and 20 by Division Method

To calculate the LCM of 4 and 20 by the division method, we will divide the numbers(4, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 20.

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

LCM of 4 and 20 by Prime Factorization

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

☛ Also Check:

LCM of 4 and 20 Examples

Example 1: The product of two numbers is 80. If their GCD is 4, what is their LCM?

Solution:

Given: GCD = 4
product of numbers = 80
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 80/4
Therefore, the LCM is 20.
The probable combination for the given case is LCM(4, 20) = 20.
Example 2: Verify the relationship between GCF and LCM of 4 and 20.

Solution:

The relation between GCF and LCM of 4 and 20 is given as,
LCM(4, 20) × GCF(4, 20) = Product of 4, 20
Prime factorization of 4 and 20 is given as, 4 = (2 × 2) = 2² and 20 = (2 × 2 × 5) = 2² × 5¹
LCM(4, 20) = 20
GCF(4, 20) = 4
LHS = LCM(4, 20) × GCF(4, 20) = 20 × 4 = 80
RHS = Product of 4, 20 = 4 × 20 = 80
⇒ LHS = RHS = 80
Hence, verified.
Example 3: The GCD and LCM of two numbers are 4 and 20 respectively. If one number is 20, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 20 × m
⇒ m = (GCD × LCM)/20
⇒ m = (4 × 20)/20
⇒ m = 4
Therefore, the other number is 4.

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FAQs on LCM of 4 and 20

What is the LCM of 4 and 20?

The LCM of 4 and 20 is 20. To find the least common multiple (LCM) of 4 and 20, we need to find the multiples of 4 and 20 (multiples of 4 = 4, 8, 12, 16 . . . . 20; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 4 and 20, i.e., 20.

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

LCM(20, 4) × GCF(20, 4) = 20 × 4
Since the LCM of 20 and 4 = 20
⇒ 20 × GCF(20, 4) = 80
Therefore, the greatest common factor = 80/20 = 4.

How to Find the LCM of 4 and 20 by Prime Factorization?

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

What is the Least Perfect Square Divisible by 4 and 20?

The least number divisible by 4 and 20 = LCM(4, 20)
LCM of 4 and 20 = 2 × 2 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 4 and 20 = LCM(4, 20) × 5 = 100 [Square root of 100 = √100 = ±10]
Therefore, 100 is the required number.

What are the Methods to Find LCM of 4 and 20?

The commonly used methods to find the LCM of 4 and 20 are:

Division Method
Listing Multiples
Prime Factorization Method

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