LCM of 12 and 16 | How to Find LCM of 12 and 16? - Coding

LCM of 12 and 16 is 48. LCM stands for Least Common Multiple and is the least common multiple of both 12 and 16. In this article, We have covered in brief, What is LCM, LCM of 12 and 16, How to find LCM of 12 and 16? and others in detail.

LCM-of-12-and-16

What is LCM?

LCM refers to a number that is a common multiple of two or more than two numbers. Note that it stands for least common multiple. It is important to tell that the number is the minimum number which when divided by two or more given numbers, leaves a remainder of zero. It is an important number for analyzing various properties.

What is LCM of 12 and 16?

Answer: LCM of 12 and 16, is 48.

Explanation:

This can be seen as 12 and 16 both divides 48 leaving 0 remainder in both cases. We can also see that there is no number less than 48 which divides both the numbers 12 and 16.

Let us see the methods to calculate the LCM of 12 and 16.

LCM of 12 and 16 Calculator

How to Find LCM of 12 and 16?

There are three methods discussed here to find the LCM of 12 and 16 that are,

LCM of 12 and 16 by Prime Factorization
LCM of 12 and 16 by Listing Multiple
LCM of 12 and 16 by Long Division

LCM of 12 and 16 by Prime Factorization

To calculate the LCM of 12 and 16, we need to enlist all the prime factors of both numbers. Then we look for multiples that are common to both numbers these are the common multiples. We expand this list until we get a number that is a common multiple of both numbers. Let us see how

Prime-Factors-of-12-16

Prime factorization of number 12

2 × 2 × 3

Prime factorization of number 16

2 × 2 × 2 × 2

LCM of 12 and 16 is

2 × 2 × 2 × 2× 3 = 48

Therefore, LCM of 12 and 16 is is 48.

LCM of 12 and 16 by Listing Multiples

We are supposed to list all the multiples of both the numbers whose LCM is to be calculated. This process is done until we find a number that is a common multiple of both 12 and 16.

Multiples of 12	Multiples of 16
12	16
24	32
36	48
48

We see that 48 is a common multiple for both 12 and 16 hence the LCM is 48.

LCM of 12 and 16 by Long Division

In LCM of 12 and 16 by Long Division, we are supposed to divide numbers by their prime factors until we can no longer further divide them. The multiplication of these divisors in the end then shows the LCM if the two numbers. Let us see this with an example of numbers 12 and 16. We will perform the long division and then multiply the factors.

LCM-of-12-and-16

LCM of (12, 16) = 2 × 2 × 2 × 2 × 3 = 48

Hence the LCM of 12 and 16 is 48

LCM vs HCF of 12 and 16

Least Common Multiple of 12 and 16 is 48 and Highest Common Factor of 12 and 16 is 4.

Also, LCM × HCF = Product of Two Numbers

12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2

LCM (12, 16) = 2 × 2 × 2 × 2 × 3 = 48

HCF (12, 16) = 2² = 4

12 × 16 = LCM (12, 16) × HCF (12, 16)

192 = 48 × 4

192 = 192

Also Check,

Example on LCM of 12 and 16

Some Examples on LCM are,

Example 1: What is LCM if the product of two numbers is 252 and their GCD is 12?

Solution:

Product of Two Numbers = 252

GCD = 12

LCM × GCD = Product of Two Numbers

LCM = (Product of Two Numbers)/GCD

LCM = 252/12

LCM = 21

Hence, LCM is 21.

Example 2: What is LCM of 15 and 20?

Solution:

Multiples of 15 and 20,

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120

Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160

Smallest number that is multiple of 15 and 20 is 60. Therefore, 60 is LCM of 15 and 20.

Practice Problems

Some practice problems on LCM are,

P1: Is 96 the LCM of 12 and 16?

P2: Find LCM of 16 and 6 using the prime factors method.

P2: Find LCM of 55 and 60 using the long division method.

FAQs on LCM of 12 and 16

What is Least Common Multiple (LCM) of 12 and 16?

LCM of 12 and 16 is 48.

What is LCM of 12, 16, and 32?

LCM of 2, 16, 32 is a number that divides all three numbers with zero remainder therefore it is number 64.

What are Methods to find LCM of 12 and 16?

Methods used to find the LCM of 24 and 36 are:

Prime Factorization Method

Long Division Method

Listing Common Factors

What are GCF and LCM of 12 and 16?

Greatest Common Factor of 12 and 16 is 4 and Least Common Multiple of 12 and 152 is 3496.

Reffered: https://www.geeksforgeeks.org

Mathematics

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