LCM of 10 and 20 - How to Find LCM of 10, 20? (2024)

LCM of 10 and 20 is the smallest number among all common multiples of 10 and 20. The first few multiples of 10 and 20 are (10, 20, 30, 40, 50, 60, . . . ) and (20, 40, 60, 80, 100, . . . ) respectively. There are 3 commonly used methods to find LCM of 10 and 20 - by prime factorization, by division method, and by listing multiples.

1.LCM of 10 and 20
2.List of Methods
3.Solved Examples
4.FAQs

What is the LCM of 10 and 20?

Answer: LCM of 10 and 20 is 20.

LCM of 10 and 20 - How to Find LCM of 10, 20? (1)

Explanation:

The LCM of two non-zero integers, x(10) and y(20), is the smallest positive integer m(20) that is divisible by both x(10) and y(20) without any remainder.

Methods to Find LCM of 10 and 20

Let's look at the different methods for finding the LCM of 10 and 20.

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

LCM of 10 and 20 by Division Method

LCM of 10 and 20 - How to Find LCM of 10, 20? (2)

To calculate the LCM of 10 and 20 by the division method, we will divide the numbers(10, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 10 and 20.

  • Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 10 and 20. Write this prime number(2) on the left of the given numbers(10 and 20), separated as per the ladder arrangement.
  • Step 2: If any of the given numbers (10, 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 10 and 20 is the product of all prime numbers on the left, i.e. LCM(10, 20) by division method = 2 × 2 × 5 = 20.

LCM of 10 and 20 by Prime Factorization

Prime factorization of 10 and 20 is (2 × 5) = 21 × 51 and (2 × 2 × 5) = 22 × 51 respectively. LCM of 10 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 51 = 20.
Hence, the LCM of 10 and 20 by prime factorization is 20.

LCM of 10 and 20 by Listing Multiples

LCM of 10 and 20 - How to Find LCM of 10, 20? (3)

To calculate the LCM of 10 and 20 by listing out the common multiples, we can follow the given below steps:

  • Step 1: List a few multiples of 10 (10, 20, 30, 40, 50, 60, . . . ) and 20 (20, 40, 60, 80, 100, . . . . )
  • Step 2: The common multiples from the multiples of 10 and 20 are 20, 40, . . .
  • Step 3: The smallest common multiple of 10 and 20 is 20.

∴ The least common multiple of 10 and 20 = 20.

☛ Also Check:

  • LCM of 63 and 21 - 63
  • LCM of 63 and 105 - 315
  • LCM of 60 and 90 - 180
  • LCM of 60 and 84 - 420
  • LCM of 60 and 80 - 240
  • LCM of 60 and 75 - 300
  • LCM of 60 and 72 - 360

FAQs on LCM of 10 and 20

What is the LCM of 10 and 20?

The LCM of 10 and 20 is 20. To find the least common multiple of 10 and 20, we need to find the multiples of 10 and 20 (multiples of 10 = 10, 20, 30, 40; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 10 and 20, i.e., 20.

If the LCM of 20 and 10 is 20, Find its GCF.

LCM(20, 10) × GCF(20, 10) = 20 × 10
Since the LCM of 20 and 10 = 20
⇒ 20 × GCF(20, 10) = 200
Therefore, the GCF (greatest common factor) = 200/20 = 10.

What are the Methods to Find LCM of 10 and 20?

The commonly used methods to find the LCM of 10 and 20 are:

  • Division Method
  • Prime Factorization Method
  • Listing Multiples

Which of the following is the LCM of 10 and 20? 11, 20, 2, 32

The value of LCM of 10, 20 is the smallest common multiple of 10 and 20. The number satisfying the given condition is 20.

What is the Least Perfect Square Divisible by 10 and 20?

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

LCM of 10 and 20 - How to Find LCM of 10, 20? (2024)

FAQs

LCM of 10 and 20 - How to Find LCM of 10, 20? ›

LCM of 10 and 20 Solved Examples

How do you find the LCM of two numbers? ›

Therefore, the formula to find LCM of two numbers is, LCM of two numbers = product of two numbers ÷ HCF of two numbers.

How do you find the LCM of each set of numbers? ›

How to find LCM by Prime Factorization
  1. Find all the prime factors of each given number.
  2. List all the prime numbers found, as many times as they occur most often for any one given number.
  3. Multiply the list of prime factors together to find the LCM.

What is the LCM of 10/20? ›

What is LCM of 10 and 20? The answer to this question is 20.

What is the LCM method example? ›

LCM denotes the least common factor or multiple of any two or more given integers. For example, L.C.M of 16 and 20 will be 2 x 2 x 2 x 2 x 5 = 80, where 80 is the smallest common multiple for numbers 16 and 20. Now, if we consider the multiples of 16 and 20, we get; 16 → 16, 32, 48, 64, 80,…

How do you find the other number of LCM? ›

Assuming that HCF = highest common factor = greatest common divisor = GCD. The product of two numbers = the product of their HCF and LCM. Example : Given one number as 80 and the HCF as 5 and LCM as 720, the other number = HCF*LCM/80 = 5*720/80 = 45.

What is the trick of LCM? ›

Trick to find the LCM of any number.

Step 1 : Take the multiple of the highest number among the numbers of which you have to find the LCM. Step 2 : Continue on multiplying till you get a number which is divisible by all three.

How is LCM calculated? ›

Step 1: Finding each number's prime factorization is the first step in computing the LCM using the prime factors approach. Step 2: When you write each number as a product of primes. Step 3: Now take the highest power of each prime number. Step 4: To obtain the LCM, multiply the prime numbers.

What is the LCM of 24 and 36? ›

The LCM of 24 and 36 is 72. To find the least common multiple of 24 and 36, we need to find the multiples of 24 and 36 (multiples of 24 = 24, 48, 72, 96; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 24 and 36, i.e., 72.

How to find LCM of 336 and 54? ›

Here the numbers in the first bracket are common primes and the numbers in the second bracket are remaining primes. Therefore, the LCM of 336 and 54 is 3024. Note: We have a shortcut for solving this problem. Therefore, the LCM of 336 and 54 is 3024.

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