LCM of 3 5 and 12

LCM of 3, 5 and 12 is 60. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest number among all frequent multiples of 3, 5, and 12 is the LCM of 3, 5, and 12. (3, 6, 9, 12, 15…), (5, 10, 15, 20, 25…), and (12, 24, 36, 48, 60…), respectively, are the first few multiples of 3, 5, and 12.

Also read: Least common multiple

What is LCM of 3, 5 and 12?

The answer to this question is 60. The LCM of 3, 5 and 12 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 3, 5 and 12, is the smallest positive integer 60 which is divisible by both 3, 5 and 12 with no remainder.

lcm of 3 5 and 12

How to Find LCM of 3, 5 and 12?

LCM of 3, 5 and 12 can be found using three methods:

  • Prime Factorisation
  • Division method
  • Listing the multiples

LCM of 3, 5 and 12 Using Prime Factorisation Method

The prime factorisation of 3, 5 and 12, respectively, is given by:

(3) = 31, (5) = 51, and

12 = (2 × 2 × 3) = 22 × 31

LCM (3, 5, 12) = 60

LCM of 3, 5 and 12 Using Division Method

We’ll divide the numbers (3, 5, 12) by their prime factors to get the LCM of 3, 5 and 12 using the division method (preferably common). The LCM of 3, 5 and 12 is calculated by multiplying these divisors.

2 3 5 12
2 3 5 6
3 3 5 3
5 1 5 1
x 1 1 1

No further division can be done.

Hence, LCM (3, 5, 12) = 120

LCM of 3, 5 and 12 Using Listing the Multiples

To calculate the LCM of 3, 5 and 12 by listing out the common multiples, list the multiples as shown below

Multiples of 3 Multiples of 5 Multiples of 12
3 5 12
6 10 24
9 15 36
…… …. ..
120 120 120

The smallest common multiple of 3, 5 and 12 is 120.

Therefore LCM Multiples of 5 = 120

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Video Lesson on Applications of LCM

LCM of 3, 5 and 12 Solved Example

Question: Find the smallest number that is divisible by 3, 5, 12 exactly.

Solution:

The value of LCM(3, 5, 12) will be the smallest number that is exactly divisible by 3, 5, and 12.

⇒ Multiples of 3, 5, and 12:

Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, . . . ., 51, 54, 57, 60, . . . .

Multiples of 5 = 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, . . . ., 45, 50, 55, 60, . . . .

Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, . . . ., 24, 36, 48, 60, . . . .

Therefore, the LCM of 3, 5, and 12 is 60.

Frequently Asked Questions on LCM of 3, 5 and 12

Q1

What is the LCM of 3, 5 and 12?

The LCM of 3, 5, and 12 is 60. To find the least common multiple (LCM) of 3, 5, and 12, we need to find the multiples of 3, 5, and 12 (multiples of 3 = 3, 6, 9, 12 . . . . 60 . . . . ; multiples of 5 = 5, 10, 15, 20 . . . . 60 . . . . ; multiples of 12 = 12, 24, 36, 48 . . . . 60 . . . . ) and choose the smallest multiple that is exactly divisible by 3, 5, and 12, i.e., 60.
Q2

List the methods used to find the LCM of 3, 5 and 12.

The methods used to find the LCM of 3, 5 and 12 are Prime Factorization Method, Division Method and Listing multiples.
Q3

What is the Relation Between GCF and LCM of 3, 5, 12?

The following equation can be used to express the relation between GCF and LCM of 3, 5, 12, i.e. LCM(3, 5, 12) = [(3 × 5 × 12) × GCF(3, 5, 12)]/[GCF(3, 5) × GCF(5, 12) × GCF(3, 12)].
Q4

How to Find the LCM of 3, 5, and 12 by Prime Factorization?

To find the LCM of 3, 5, and 12 using prime factorization, we will find the prime factors, (3 = 3), (5 = 5), and (12 = 2 × 2 × 3). LCM of 3, 5, and 12 is the product of prime factors raised to their respective highest exponent among the numbers 3, 5, and 12.
⇒ LCM of 3, 5, 12 = 2 × 2 × 3 × 5 = 60.
Q5

Which of the following is the LCM of 3, 5, and 12? 28, 36, 96, 60

The value of LCM of 3, 5, 12 is the smallest common multiple of 3, 5, and 12. The number satisfying the given condition is 60.

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