LCM of 46 and 51 is 2346. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Among all common multiples of 46 and 51, the LCM of 46 and 51 is the smallest number. (46, 92, 138, 184, 230, 276, etc.) and (51, 102, 153, 204, 255, 306, etc.) are the first few multiples of 46 and 51, respectively. The division method, listing multiples, and prime factorization are the three most prevalent methods for calculating the LCM of 46 and 51.
Also read: Least common multiple
What is LCM of 46 and 51?
The answer to this question is 2346. The LCM of 46 and 51 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 46 and 51, is the smallest positive integer 2346 which is divisible by both 46 and 51 with no remainder.
How to Find LCM of 46 and 51?
LCM of 46 and 51 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 46 and 51 Using Prime Factorisation Method
The prime factorisation of 46 and 51, respectively, is given by:
46 = (2 × 23) = 21 × 231 and
51 = (3 × 17) = 31 × 171
LCM (46, 51) = 2346
LCM of 46 and 51 Using Division Method
We’ll divide the numbers (46, 51) by their prime factors to get the LCM of 46 and 51 using the division method (preferably common). The LCM of 46 and 51 is calculated by multiplying these divisors.
| 2 | 46 | 51 |
| 3 | 23 | 51 |
| 17 | 23 | 17 |
| 23 | 23 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (46, 51) = 2346
LCM of 46 and 51 Using Listing the Multiples
To calculate the LCM of 46 and 51 by listing out the common multiples, list the multiples as shown below
| Multiples of 46 | Multiples of 51 |
| 46 | 51 |
| 92 | 102 |
| 138 | 153 |
| ……. | …… |
| 2346 | 2346 |
The smallest common multiple of 46 and 51 is 2346.
Therefore LCM (46, 51) = 2346
Related Articles
Video Lesson on Applications of LCM
LCM of 46 and 51 Solved Example
Question: The product of two numbers is 2346. If their GCD is 1, what is their LCM?
Solution:
Given: GCD = 1
product of numbers = 2346
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 2346/1
Therefore, the LCM is 2346.
The probable combination for the given case is LCM(46, 51) = 2346.
Frequently Asked Questions on LCM of 46 and 51
What is the LCM of 46 and 51?
List the methods used to find the LCM of 46 and 51.
What is the Relation Between GCF and LCM of 46, 51?
If the LCM of 51 and 46 is 2346, Find its GCF.
Since the LCM of 51 and 46 = 2346
⇒ 2346 × GCF(51, 46) = 2346
Therefore, the GCF = 2346/2346 = 1.
Comments