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.
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
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
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.
