LCM of 20 and 36

LCM of 20 and 36 is the smallest number among all common multiples of 20 and 36. The first few multiples of 20 and 36 are (20, 40, 60, 80, 100, . . . ) and (36, 72, 108, 144, 180, 216, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 36 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 20 and 36 is 180.

Explanation:

The LCM of two non-zero integers, x(20) and y(36), is the smallest positive integer m(180) that is divisible by both x(20) and y(36) without any remainder.

Let's look at the different methods for finding the LCM of 20 and 36.

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

LCM of 20 and 36 by Prime Factorization

Prime factorization of 20 and 36 is (2 × 2 × 5) = 2² × 5¹ and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 20 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3² × 5¹ = 180.
Hence, the LCM of 20 and 36 by prime factorization is 180.

LCM of 20 and 36 by Division Method

To calculate the LCM of 20 and 36 by the division method, we will divide the numbers(20, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 36.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 36. Write this prime number(2) on the left of the given numbers(20 and 36), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (20, 36) 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 36 is the product of all prime numbers on the left, i.e. LCM(20, 36) by division method = 2 × 2 × 3 × 3 × 5 = 180.

LCM of 20 and 36 by Listing Multiples

To calculate the LCM of 20 and 36 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, . . . ) and 36 (36, 72, 108, 144, 180, 216, . . . . )
• Step 2: The common multiples from the multiples of 20 and 36 are 180, 360, . . .
• Step 3: The smallest common multiple of 20 and 36 is 180.

∴ The least common multiple of 20 and 36 = 180.

☛ Also Check:

• LCM of 48, 56 and 72 - 1008
• LCM of 30 and 54 - 270
• LCM of 6, 9 and 12 - 36
• LCM of 4, 6 and 10 - 60
• LCM of 6, 9 and 15 - 90
• LCM of 42 and 63 - 126
• LCM of 64 and 96 - 192

FAQs on LCM of 20 and 36

What is the LCM of 20 and 36?

The LCM of 20 and 36 is 180. To find the least common multiple (LCM) of 20 and 36, we need to find the multiples of 20 and 36 (multiples of 20 = 20, 40, 60, 80 . . . . 180; multiples of 36 = 36, 72, 108, 144 . . . . 180) and choose the smallest multiple that is exactly divisible by 20 and 36, i.e., 180.

What are the Methods to Find LCM of 20 and 36?

The commonly used methods to find the LCM of 20 and 36 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

What is the Least Perfect Square Divisible by 20 and 36?

The least number divisible by 20 and 36 = LCM(20, 36)
LCM of 20 and 36 = 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 20 and 36 = LCM(20, 36) × 5 = 900 [Square root of 900 = √900 = ±30]
Therefore, 900 is the required number.

If the LCM of 36 and 20 is 180, Find its GCF.

LCM(36, 20) × GCF(36, 20) = 36 × 20
Since the LCM of 36 and 20 = 180
⇒ 180 × GCF(36, 20) = 720
Therefore, the greatest common factor = 720/180 = 4.

How to Find the LCM of 20 and 36 by Prime Factorization?

To find the LCM of 20 and 36 using prime factorization, we will find the prime factors, (20 = 2 × 2 × 5) and (36 = 2 × 2 × 3 × 3). LCM of 20 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 20 and 36.
⇒ LCM of 20, 36 = 2² × 3² × 5¹ = 180.