LCM of 3 and 4 is the smallest number among all common multiples of 3 and 4. The first few multiples of 3 and 4 are (3, 6, 9, 12, 15, 18, 21, . . . ) and (4, 8, 12, 16, 20, . . . ) respectively. There are 3 commonly used methods to find LCM of 3 and 4 - by listing multiples, by division method, and by prime factorization.
| 1. | LCM of 3 and 4 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 3 and 4?
Answer: LCM of 3 and 4 is 12.
Explanation:
The LCM of two non-zero integers, x(3) and y(4), is the smallest positive integer m(12) that is divisible by both x(3) and y(4) without any remainder.
Methods to Find LCM of 3 and 4
The methods to find the LCM of 3 and 4 are explained below.
- By Listing Multiples
- By Division Method
- By Prime Factorization Method
LCM of 3 and 4 by Listing Multiples
To calculate the LCM of 3 and 4 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 3 (3, 6, 9, 12, 15, 18, 21, . . . ) and 4 (4, 8, 12, 16, 20, . . . . )
- Step 2: The common multiples from the multiples of 3 and 4 are 12, 24, . . .
- Step 3: The smallest common multiple of 3 and 4 is 12.
∴ The least common multiple of 3 and 4 = 12.
LCM of 3 and 4 by Division Method
To calculate the LCM of 3 and 4 by the division method, we will divide the numbers(3, 4) by their prime factors (preferably common). The product of these divisors gives the LCM of 3 and 4.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 3 and 4. Write this prime number(2) on the left of the given numbers(3 and 4), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (3, 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 3 and 4 is the product of all prime numbers on the left, i.e. LCM(3, 4) by division method = 2 × 2 × 3 = 12.
LCM of 3 and 4 by Prime Factorization
Prime factorization of 3 and 4 is (3) = 31 and (2 × 2) = 22 respectively. LCM of 3 and 4 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 31 = 12.
Hence, the LCM of 3 and 4 by prime factorization is 12.
☛ Also Check:
- LCM of 60 and 72 - 360
- LCM of 6, 7 and 8 - 168
- LCM of 5, 6 and 10 - 30
- LCM of 8 and 10 - 40
- LCM of 8, 12, 15 and 20 - 120
- LCM of 10 and 100 - 100
- LCM of 8, 12 and 24 - 24
FAQs on LCM of 3 and 4
What is the LCM of 3 and 4?
The LCM of 3 and 4 is 12. To find the LCM of 3 and 4, we need to find the multiples of 3 and 4 (multiples of 3 = 3, 6, 9, 12; multiples of 4 = 4, 8, 12, 16) and choose the smallest multiple that is exactly divisible by 3 and 4, i.e., 12.
What is the Relation Between GCF and LCM of 3, 4?
The following equation can be used to express the relation between GCF and LCM of 3 and 4, i.e. GCF × LCM = 3 × 4.
If the LCM of 4 and 3 is 12, Find its GCF.
LCM(4, 3) × GCF(4, 3) = 4 × 3
Since the LCM of 4 and 3 = 12
⇒ 12 × GCF(4, 3) = 12
Therefore, the greatest common factor (GCF) = 12/12 = 1.
Which of the following is the LCM of 3 and 4? 42, 28, 12, 36
The value of LCM of 3, 4 is the smallest common multiple of 3 and 4. The number satisfying the given condition is 12.
What are the Methods to Find LCM of 3 and 4?
The commonly used methods to find the LCM of 3 and 4 are:
- Listing Multiples
- Prime Factorization Method
- Division Method
