LCM of 6 and 20

LCM of 6 and 20 is the smallest number among all common multiples of 6 and 20. The first few multiples of 6 and 20 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (20, 40, 60, 80, 100, 120, 140, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 20 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 6 and 20 is 60.

Explanation:

The LCM of two non-zero integers, x(6) and y(20), is the smallest positive integer m(60) that is divisible by both x(6) and y(20) without any remainder.

The methods to find the LCM of 6 and 20 are explained below.

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

LCM of 6 and 20 by Division Method

To calculate the LCM of 6 and 20 by the division method, we will divide the numbers(6, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 20.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 20. Write this prime number(2) on the left of the given numbers(6 and 20), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 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 6 and 20 is the product of all prime numbers on the left, i.e. LCM(6, 20) by division method = 2 × 2 × 3 × 5 = 60.

LCM of 6 and 20 by Prime Factorization

Prime factorization of 6 and 20 is (2 × 3) = 2¹ × 3¹ and (2 × 2 × 5) = 2² × 5¹ respectively. LCM of 6 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ = 60.
Hence, the LCM of 6 and 20 by prime factorization is 60.

LCM of 6 and 20 by Listing Multiples

To calculate the LCM of 6 and 20 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . ) and 20 (20, 40, 60, 80, 100, 120, 140, . . . . )
• Step 2: The common multiples from the multiples of 6 and 20 are 60, 120, . . .
• Step 3: The smallest common multiple of 6 and 20 is 60.

∴ The least common multiple of 6 and 20 = 60.

☛ Also Check:

• LCM of 19 and 57 - 57
• LCM of 60 and 90 - 180
• LCM of 25 and 30 - 150
• LCM of 60 and 62 - 1860
• LCM of 21 and 30 - 210
• LCM of 25 and 36 - 900
• LCM of 28, 36, 45 and 60 - 1260

FAQs on LCM of 6 and 20

What is the LCM of 6 and 20?

The LCM of 6 and 20 is 60. To find the least common multiple (LCM) of 6 and 20, we need to find the multiples of 6 and 20 (multiples of 6 = 6, 12, 18, 24 . . . . 60; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 6 and 20, i.e., 60.

If the LCM of 20 and 6 is 60, Find its GCF.

LCM(20, 6) × GCF(20, 6) = 20 × 6
Since the LCM of 20 and 6 = 60
⇒ 60 × GCF(20, 6) = 120
Therefore, the GCF (greatest common factor) = 120/60 = 2.

What is the Relation Between GCF and LCM of 6, 20?

The following equation can be used to express the relation between GCF and LCM of 6 and 20, i.e. GCF × LCM = 6 × 20.

How to Find the LCM of 6 and 20 by Prime Factorization?

To find the LCM of 6 and 20 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (20 = 2 × 2 × 5). LCM of 6 and 20 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 20.
⇒ LCM of 6, 20 = 2² × 3¹ × 5¹ = 60.

What are the Methods to Find LCM of 6 and 20?

The commonly used methods to find the LCM of 6 and 20 are:

• Division Method
• Prime Factorization Method
• Listing Multiples