Lcd Of 16 And 12

LCM of 12 and 16

LCM of 12 and 16 is the smallest number among all common multiples of 12 and xvi. The outset few multiples of 12 and xvi are (12, 24, 36, 48, 60, 72, . . . ) and (16, 32, 48, 64, lxxx, 96, 112, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 16 - past prime factorization, by list multiples, and by division method.

one.	LCM of 12 and 16
2.	List of Methods
3.	Solved Examples
iv.	FAQs

What is the LCM of 12 and 16?

Answer: LCM of 12 and 16 is 48.

LCM of 12 and 16

Explanation:

The LCM of two non-zilch integers, x(12) and y(xvi), is the smallest positive integer m(48) that is divisible past both x(12) and y(16) without any residuum.

Methods to Discover LCM of 12 and 16

Let's await at the unlike methods for finding the LCM of 12 and xvi.

Past Listing Multiples
By Division Method
Past Prime Factorization Method

LCM of 12 and sixteen by Listing Multiples

LCM of 12 and 16 by Listing Multiples Method

To calculate the LCM of 12 and sixteen past listing out the mutual multiples, nosotros can follow the given beneath steps:

Step 1: Listing a few multiples of 12 (12, 24, 36, 48, 60, 72, . . . ) and 16 (sixteen, 32, 48, 64, 80, 96, 112, . . . . )
Step 2: The mutual multiples from the multiples of 12 and 16 are 48, 96, . . .
Step iii: The smallest common multiple of 12 and xvi is 48.

∴ The to the lowest degree mutual multiple of 12 and 16 = 48.

LCM of 12 and 16 past Division Method

To calculate the LCM of 12 and 16 past the division method, nosotros will separate the numbers(12, 16) by their prime factors (preferably common). The production of these divisors gives the LCM of 12 and 16.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and sixteen. Write this prime number(2) on the left of the given numbers(12 and sixteen), separated as per the ladder arrangement.
Stride 2: If any of the given numbers (12, xvi) is a multiple of 2, split it by 2 and write the quotient beneath it. Bring down any number that is not divisible by the prime number.
Step 3: Keep the steps until simply 1s are left in the last row.

The LCM of 12 and 16 is the product of all prime numbers on the left, i.e. LCM(12, 16) by division method = ii × 2 × 2 × 2 × three = 48.

LCM of 12 and 16 by Prime Factorization

Prime factorization of 12 and 16 is (2 × two × 3) = 2ⁱⁱ × 3^one and (2 × 2 × ii × two) = 2⁴ respectively. LCM of 12 and sixteen can be obtained by multiplying prime factors raised to their respective highest ability, i.e. 2⁴ × iii^ane = 48.
Hence, the LCM of 12 and 16 by prime factorization is 48.

☛ Also Check:

LCM of sixteen and 32 - 32
LCM of 16 and thirty - 240
LCM of 16 and 28 - 112
LCM of 16 and 24 - 48
LCM of 16 and 22 - 176
LCM of 16 and xx - eighty
LCM of 16 and 18 - 144

FAQs on LCM of 12 and 16

What is the LCM of 12 and 16?

The LCM of 12 and 16 is 48 . To detect the LCM (least common multiple) of 12 and xvi, nosotros need to observe the multiples of 12 and 16 (multiples of 12 = 12, 24, 36, 48; multiples of 16 = 16, 32, 48, 64) and choose the smallest multiple that is exactly divisible past 12 and 16, i.e., 48.

If the LCM of sixteen and 12 is 48, Find its GCF.

LCM(16, 12) × GCF(16, 12) = 16 × 12
Since the LCM of 16 and 12 = 48
⇒ 48 × GCF(xvi, 12) = 192
Therefore, the GCF = 192/48 = iv.

Which of the post-obit is the LCM of 12 and xvi? 35, 42, 48, 32

The value of LCM of 12, 16 is the smallest common multiple of 12 and 16. The number satisfying the given condition is 48.

How to Find the LCM of 12 and sixteen by Prime Factorization?

To find the LCM of 12 and 16 using prime factorization, we will observe the prime factors, (12 = two × two × iii) and (16 = 2 × 2 × 2 × 2). LCM of 12 and sixteen is the product of prime number factors raised to their corresponding highest exponent amid the numbers 12 and sixteen.
⇒ LCM of 12, 16 = ii⁴ × iii¹ = 48.

What is the To the lowest degree Perfect Foursquare Divisible by 12 and 16?

The least number divisible by 12 and 16 = LCM(12, 16)
LCM of 12 and sixteen = two × 2 × 2 × ii × 3 [Incomplete pair(south): 3]
⇒ Least perfect square divisible by each 12 and 16 = LCM(12, xvi) × iii = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.