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LCM of 33 and 44

LCM of 33 and 44 is the smallest number among all common multiples of 33 and 44. The first few multiples of 33 and 44 are (33, 66, 99, 132, 165, 198, 231, . . . ) and (44, 88, 132, 176, . . . ) respectively. There are 3 commonly used methods to find LCM of 33 and 44 - by division method, by listing multiples, and by prime factorization.

1.	LCM of 33 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is the LCM of 33 and 44?

Answer: LCM of 33 and 44 is 132.

Explanation:

The LCM of two non-zero integers, x(33) and y(44), is the smallest positive integer m(132) that is divisible by both x(33) and y(44) without any remainder.

Methods to Find LCM of 33 and 44

Let's look at the different methods for finding the LCM of 33 and 44.

By Division Method
By Prime Factorization Method
By Listing Multiples

LCM of 33 and 44 by Division Method

To calculate the LCM of 33 and 44 by the division method, we will divide the numbers(33, 44) by their prime factors (preferably common). The product of these divisors gives the LCM of 33 and 44.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 33 and 44. Write this prime number(2) on the left of the given numbers(33 and 44), separated as per the ladder arrangement.
Step 2: If any of the given numbers (33, 44) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 33 and 44 is the product of all prime numbers on the left, i.e. LCM(33, 44) by division method = 2 × 2 × 3 × 11 = 132.

LCM of 33 and 44 by Prime Factorization

Prime factorization of 33 and 44 is (3 × 11) = 3¹ × 11¹ and (2 × 2 × 11) = 2² × 11¹ respectively. LCM of 33 and 44 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 11¹ = 132.
Hence, the LCM of 33 and 44 by prime factorization is 132.

LCM of 33 and 44 by Listing Multiples

To calculate the LCM of 33 and 44 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 33 (33, 66, 99, 132, 165, 198, 231, . . . ) and 44 (44, 88, 132, 176, . . . . )
Step 2: The common multiples from the multiples of 33 and 44 are 132, 264, . . .
Step 3: The smallest common multiple of 33 and 44 is 132.

∴ The least common multiple of 33 and 44 = 132.

☛ Also Check:

LCM of 33 and 44 Examples

Example 1: The GCD and LCM of two numbers are 11 and 132 respectively. If one number is 44, find the other number.

Solution:

Let the other number be m.
∵ GCD × LCM = 44 × m
⇒ m = (GCD × LCM)/44
⇒ m = (11 × 132)/44
⇒ m = 33
Therefore, the other number is 33.
Example 2: Verify the relationship between GCF and LCM of 33 and 44.

Solution:

The relation between GCF and LCM of 33 and 44 is given as,
LCM(33, 44) × GCF(33, 44) = Product of 33, 44
Prime factorization of 33 and 44 is given as, 33 = (3 × 11) = 3¹ × 11¹ and 44 = (2 × 2 × 11) = 2² × 11¹
LCM(33, 44) = 132
GCF(33, 44) = 11
LHS = LCM(33, 44) × GCF(33, 44) = 132 × 11 = 1452
RHS = Product of 33, 44 = 33 × 44 = 1452
⇒ LHS = RHS = 1452
Hence, verified.
Example 3: The product of two numbers is 1452. If their GCD is 11, what is their LCM?

Solution:

Given: GCD = 11
product of numbers = 1452
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1452/11
Therefore, the LCM is 132.
The probable combination for the given case is LCM(33, 44) = 132.

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FAQs on LCM of 33 and 44

What is the LCM of 33 and 44?

The LCM of 33 and 44 is 132. To find the LCM of 33 and 44, we need to find the multiples of 33 and 44 (multiples of 33 = 33, 66, 99, 132; multiples of 44 = 44, 88, 132, 176) and choose the smallest multiple that is exactly divisible by 33 and 44, i.e., 132.

How to Find the LCM of 33 and 44 by Prime Factorization?

To find the LCM of 33 and 44 using prime factorization, we will find the prime factors, (33 = 3 × 11) and (44 = 2 × 2 × 11). LCM of 33 and 44 is the product of prime factors raised to their respective highest exponent among the numbers 33 and 44.
⇒ LCM of 33, 44 = 2² × 3¹ × 11¹ = 132.

Which of the following is the LCM of 33 and 44? 132, 36, 11, 3

The value of LCM of 33, 44 is the smallest common multiple of 33 and 44. The number satisfying the given condition is 132.

What is the Least Perfect Square Divisible by 33 and 44?

The least number divisible by 33 and 44 = LCM(33, 44)
LCM of 33 and 44 = 2 × 2 × 3 × 11 [Incomplete pair(s): 3, 11]
⇒ Least perfect square divisible by each 33 and 44 = LCM(33, 44) × 3 × 11 = 4356 [Square root of 4356 = √4356 = ±66]
Therefore, 4356 is the required number.

If the LCM of 44 and 33 is 132, Find its GCF.

LCM(44, 33) × GCF(44, 33) = 44 × 33
Since the LCM of 44 and 33 = 132
⇒ 132 × GCF(44, 33) = 1452
Therefore, the greatest common factor (GCF) = 1452/132 = 11.

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