LCM of 20 and 28

LCM of 20 and 28 is the smallest number among all common multiples of 20 and 28. The first few multiples of 20 and 28 are (20, 40, 60, 80, 100, 120, . . . ) and (28, 56, 84, 112, 140, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 28 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 20 and 28 is 140.

Explanation:

The LCM of two non-zero integers, x(20) and y(28), is the smallest positive integer m(140) that is divisible by both x(20) and y(28) without any remainder.

Let's look at the different methods for finding the LCM of 20 and 28.

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

LCM of 20 and 28 by Listing Multiples

To calculate the LCM of 20 and 28 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 20 (20, 40, 60, 80, 100, 120, . . . ) and 28 (28, 56, 84, 112, 140, . . . . )
• Step 2: The common multiples from the multiples of 20 and 28 are 140, 280, . . .
• Step 3: The smallest common multiple of 20 and 28 is 140.

∴ The least common multiple of 20 and 28 = 140.

LCM of 20 and 28 by Division Method

To calculate the LCM of 20 and 28 by the division method, we will divide the numbers(20, 28) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 28.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 28. Write this prime number(2) on the left of the given numbers(20 and 28), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (20, 28) 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 20 and 28 is the product of all prime numbers on the left, i.e. LCM(20, 28) by division method = 2 × 2 × 5 × 7 = 140.

LCM of 20 and 28 by Prime Factorization

Prime factorization of 20 and 28 is (2 × 2 × 5) = 2² × 5¹ and (2 × 2 × 7) = 2² × 7¹ respectively. LCM of 20 and 28 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5¹ × 7¹ = 140.
Hence, the LCM of 20 and 28 by prime factorization is 140.

☛ Also Check:

• LCM of 5, 6 and 8 - 120
• LCM of 12 and 14 - 84
• LCM of 6, 8 and 15 - 120
• LCM of 12 and 45 - 180
• LCM of 2601 and 2616 - 2268072
• LCM of 7 and 49 - 49
• LCM of 6 and 12 - 12

FAQs on LCM of 20 and 28

What is the LCM of 20 and 28?

The LCM of 20 and 28 is 140. To find the LCM (least common multiple) of 20 and 28, we need to find the multiples of 20 and 28 (multiples of 20 = 20, 40, 60, 80 . . . . 140; multiples of 28 = 28, 56, 84, 112 . . . . 140) and choose the smallest multiple that is exactly divisible by 20 and 28, i.e., 140.

If the LCM of 28 and 20 is 140, Find its GCF.

LCM(28, 20) × GCF(28, 20) = 28 × 20
Since the LCM of 28 and 20 = 140
⇒ 140 × GCF(28, 20) = 560
Therefore, the greatest common factor = 560/140 = 4.

What is the Relation Between GCF and LCM of 20, 28?

The following equation can be used to express the relation between GCF and LCM of 20 and 28, i.e. GCF × LCM = 20 × 28.

What are the Methods to Find LCM of 20 and 28?

The commonly used methods to find the LCM of 20 and 28 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

Which of the following is the LCM of 20 and 28? 11, 32, 140, 27

The value of LCM of 20, 28 is the smallest common multiple of 20 and 28. The number satisfying the given condition is 140.