LCM of 8 and 20

LCM of 8 and 20 is the smallest number among all common multiples of 8 and 20. The first few multiples of 8 and 20 are (8, 16, 24, 32, . . . ) and (20, 40, 60, 80, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 20 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 8 and 20 is 40.

Explanation:

The LCM of two non-zero integers, x(8) and y(20), is the smallest positive integer m(40) that is divisible by both x(8) and y(20) without any remainder.

Let's look at the different methods for finding the LCM of 8 and 20.

• By Listing Multiples
• By Division Method
• By Prime Factorization Method

LCM of 8 and 20 by Listing Multiples

To calculate the LCM of 8 and 20 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, . . . ) and 20 (20, 40, 60, 80, 100, . . . . )
• Step 2: The common multiples from the multiples of 8 and 20 are 40, 80, . . .
• Step 3: The smallest common multiple of 8 and 20 is 40.

∴ The least common multiple of 8 and 20 = 40.

LCM of 8 and 20 by Division Method

To calculate the LCM of 8 and 20 by the division method, we will divide the numbers(8, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 20.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 20. Write this prime number(2) on the left of the given numbers(8 and 20), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 20 is the product of all prime numbers on the left, i.e. LCM(8, 20) by division method = 2 × 2 × 2 × 5 = 40.

LCM of 8 and 20 by Prime Factorization

Prime factorization of 8 and 20 is (2 × 2 × 2) = 2³ and (2 × 2 × 5) = 2² × 5¹ respectively. LCM of 8 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 5¹ = 40.
Hence, the LCM of 8 and 20 by prime factorization is 40.

☛ Also Check:

• LCM of 48, 56 and 72 - 1008
• LCM of 16, 24, 36 and 54 - 432
• LCM of 12, 18 and 20 - 180
• LCM of 9 and 21 - 63
• LCM of 3, 9 and 12 - 36
• LCM of 40 and 60 - 120
• LCM of 24 and 40 - 120

FAQs on LCM of 8 and 20

What is the LCM of 8 and 20?

The LCM of 8 and 20 is 40. To find the LCM of 8 and 20, we need to find the multiples of 8 and 20 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 8 and 20, i.e., 40.

What are the Methods to Find LCM of 8 and 20?

The commonly used methods to find the LCM of 8 and 20 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Least Perfect Square Divisible by 8 and 20?

The least number divisible by 8 and 20 = LCM(8, 20)
LCM of 8 and 20 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 8 and 20 = LCM(8, 20) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

If the LCM of 20 and 8 is 40, Find its GCF.

LCM(20, 8) × GCF(20, 8) = 20 × 8
Since the LCM of 20 and 8 = 40
⇒ 40 × GCF(20, 8) = 160
Therefore, the GCF (greatest common factor) = 160/40 = 4.

How to Find the LCM of 8 and 20 by Prime Factorization?

To find the LCM of 8 and 20 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (20 = 2 × 2 × 5). LCM of 8 and 20 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 20.
⇒ LCM of 8, 20 = 2³ × 5¹ = 40.