LCM of 2 and 4 is the smallest number among all common multiples of 2 and 4. The first few multiples of 2 and 4 are (2, 4, 6, 8, 10, . . . ) and (4, 8, 12, 16, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 4 - by listing multiples, by division method, and by prime factorization.
| 1. | LCM of 2 and 4 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 2 and 4?
Answer: LCM of 2 and 4 is 4.
Explanation:
The LCM of two non-zero integers, x(2) and y(4), is the smallest positive integer m(4) that is divisible by both x(2) and y(4) without any remainder.
Methods to Find LCM of 2 and 4
Let's look at the different methods for finding the LCM of 2 and 4.
- By Prime Factorization Method
- By Listing Multiples
- By Division Method
LCM of 2 and 4 by Prime Factorization
Prime factorization of 2 and 4 is (2) = 21 and (2 × 2) = 22 respectively. LCM of 2 and 4 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 = 4.
Hence, the LCM of 2 and 4 by prime factorization is 4.
LCM of 2 and 4 by Listing Multiples
To calculate the LCM of 2 and 4 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, . . . ) and 4 (4, 8, 12, 16, . . . . )
- Step 2: The common multiples from the multiples of 2 and 4 are 4, 8, . . .
- Step 3: The smallest common multiple of 2 and 4 is 4.
∴ The least common multiple of 2 and 4 = 4.
LCM of 2 and 4 by Division Method
To calculate the LCM of 2 and 4 by the division method, we will divide the numbers(2, 4) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 4.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 4. Write this prime number(2) on the left of the given numbers(2 and 4), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (2, 4) 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 2 and 4 is the product of all prime numbers on the left, i.e. LCM(2, 4) by division method = 2 × 2 = 4.
☛ Also Check:
- LCM of 14 and 15 - 210
- LCM of 5, 9 and 15 - 45
- LCM of 72 and 84 - 504
- LCM of 18, 24 and 36 - 72
- LCM of 24 and 64 - 192
- LCM of 15 and 27 - 135
- LCM of 7, 11, 21 and 22 - 462
FAQs on LCM of 2 and 4
What is the LCM of 2 and 4?
The LCM of 2 and 4 is 4. To find the least common multiple of 2 and 4, we need to find the multiples of 2 and 4 (multiples of 2 = 2, 4, 6, 8; multiples of 4 = 4, 8, 12, 16) and choose the smallest multiple that is exactly divisible by 2 and 4, i.e., 4.
How to Find the LCM of 2 and 4 by Prime Factorization?
To find the LCM of 2 and 4 using prime factorization, we will find the prime factors, (2 = 2) and (4 = 2 × 2). LCM of 2 and 4 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 4.
⇒ LCM of 2, 4 = 22 = 4.
If the LCM of 4 and 2 is 4, Find its GCF.
LCM(4, 2) × GCF(4, 2) = 4 × 2
Since the LCM of 4 and 2 = 4
⇒ 4 × GCF(4, 2) = 8
Therefore, the GCF (greatest common factor) = 8/4 = 2.
What is the Relation Between GCF and LCM of 2, 4?
The following equation can be used to express the relation between GCF and LCM of 2 and 4, i.e. GCF × LCM = 2 × 4.
Which of the following is the LCM of 2 and 4? 5, 4, 30, 32
The value of LCM of 2, 4 is the smallest common multiple of 2 and 4. The number satisfying the given condition is 4.
