LCM of 3 and 30

LCM of 3 and 30 is 30. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all common multiples of 3 and 30 is the LCM of 3 and 30. (3, 6, 9, 12,… ) and (30, 60, 90, 120, 150, 180,… ) are the first few multiples of 3 and 30, respectively. To find the LCM of 3 and 30, there are three typical methods: listing multiples, division method, and prime factorization.

Also read: Least common multiple

What is LCM of 3 and 30?

The answer to this question is 30. The LCM of 3 and 30 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3 and 30, is the smallest positive integer 30 which is divisible by both 3 and 30 with no remainder.

lcm of 3 and 30

How to Find LCM of 3 and 30?

LCM of 3 and 30 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 3 and 30 Using Prime Factorisation Method

The prime factorisation of 3 and 30, respectively, is given by:

3 = 31 and

30 = (2 × 3 × 5) = 21 × 31 × 51

LCM (3, 30) = 30

LCM of 3 and 30 Using Division Method

We’ll divide the numbers (3, 30) by their prime factors to get the LCM of 3 and 30 using the division method (preferably common). The LCM of 3 and 30 is calculated by multiplying these divisors.

2 3 30
3 3 15
5 1 5
x 1 1

No further division can be done.

Hence, LCM (3, 30) = 30

LCM of 3 and 30 Using Listing the Multiples

To calculate the LCM of 3 and 30 by listing out the common multiples, list the multiples as shown below

Multiples of 3 Multiples of 30
3 30
6 60
9 90
…. 120
30 150

The smallest common multiple of 3 and 30 is 30.

Therefore LCM (3, 30) = 30

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Video Lesson on Applications of LCM

LCM of 3 and 30 Solved Example

Question: The product of two numbers is 90. If their GCD is 3, what is their LCM?

Solution:

Given: GCD = 3

product of numbers = 90

∵ LCM × GCD = product of numbers

⇒ LCM = Product/GCD = 90/3

Therefore, the LCM is 30.

The probable combination for the given case is LCM(3, 30) = 30.

Frequently Asked Questions on LCM of 3 and 30

Q1

What is the LCM of 3 and 30?

The LCM of 3 and 30 is 30. To find the least common multiple (LCM) of 3 and 30, we need to find the multiples of 3 and 30 (multiples of 3 = 3, 6, 9, 12 . . . . 30; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 3 and 30, i.e., 30.
Q2

List the methods used to find the LCM of 3 and 30.

The methods used to find the LCM of 3 and 30 are the Prime Factorization Method, Division Method and Listing multiples.
Q3

If the LCM of 30 and 3 is 30, Find its GCF.

LCM(30, 3) × GCF(30, 3) = 30 × 3
Since the LCM of 30 and 3 = 30
⇒ 30 × GCF(30, 3) = 90
Therefore, the greatest common factor = 90/30 = 3.
Q4

How to Find the LCM of 3 and 30 by Prime Factorization?

To find the LCM of 3 and 30 using prime factorization, we will find the prime factors, (3 = 3) and (30 = 2 × 3 × 5). The LCM of 3 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 3 and 30.
⇒ LCM of 3, 30 = 2 × 3 × 5 = 30.
Q5

What is the Relation Between GCF and LCM of 3, 30?

The following equation can be used to express the relation between GCF and LCM of 3 and 30, i.e. GCF × LCM = 3 × 30.

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