LCM of 46 and 51

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.

lcm of 46 and 51

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

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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

Q1

What is the LCM of 46 and 51?

The LCM of 46 and 51 is 2346. To find the least common multiple (LCM) of 46 and 51, we need to find the multiples of 46 and 51 (multiples of 46 = 46, 92, 138, 184 . . . . 2346; multiples of 51 = 51, 102, 153, 204 . . . . 2346) and choose the smallest multiple that is exactly divisible by 46 and 51, i.e., 2346.
Q2

List the methods used to find the LCM of 46 and 51.

The methods used to find the LCM of 46 and 51 are Prime Factorization Method, Division Method and Listing multiples.
Q3

What is the Relation Between GCF and LCM of 46, 51?

The following equation can be used to express the relation between GCF and LCM of 46 and 51, i.e. GCF × LCM = 46 × 51.
Q4

If the LCM of 51 and 46 is 2346, Find its GCF.

LCM(51, 46) × GCF(51, 46) = 51 × 46
Since the LCM of 51 and 46 = 2346
⇒ 2346 × GCF(51, 46) = 2346
Therefore, the GCF = 2346/2346 = 1.
Q5

Which of the following is the LCM of 46 and 51? 15, 24, 28, 2346

The value of LCM of 46, 51 is the smallest common multiple of 46 and 51. The number satisfying the given condition is 2346.

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