LCM of 22 and 33

LCM of 22 and 33 is the smallest number among all common multiples of 22 and 33. The first few multiples of 22 and 33 are (22, 44, 66, 88, 110, 132, . . . ) and (33, 66, 99, 132, 165, . . . ) respectively. There are 3 commonly used methods to find LCM of 22 and 33 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 22 and 33 is 66.

Explanation:

The LCM of two non-zero integers, x(22) and y(33), is the smallest positive integer m(66) that is divisible by both x(22) and y(33) without any remainder.

The methods to find the LCM of 22 and 33 are explained below.

• By Prime Factorization Method
• By Listing Multiples
• By Division Method

LCM of 22 and 33 by Prime Factorization

Prime factorization of 22 and 33 is (2 × 11) = 2¹ × 11¹ and (3 × 11) = 3¹ × 11¹ respectively. LCM of 22 and 33 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 11¹ = 66.
Hence, the LCM of 22 and 33 by prime factorization is 66.

LCM of 22 and 33 by Listing Multiples

To calculate the LCM of 22 and 33 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 22 (22, 44, 66, 88, 110, 132, . . . ) and 33 (33, 66, 99, 132, 165, . . . . )
• Step 2: The common multiples from the multiples of 22 and 33 are 66, 132, . . .
• Step 3: The smallest common multiple of 22 and 33 is 66.

∴ The least common multiple of 22 and 33 = 66.

LCM of 22 and 33 by Division Method

To calculate the LCM of 22 and 33 by the division method, we will divide the numbers(22, 33) by their prime factors (preferably common). The product of these divisors gives the LCM of 22 and 33.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 22 and 33. Write this prime number(2) on the left of the given numbers(22 and 33), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (22, 33) 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 22 and 33 is the product of all prime numbers on the left, i.e. LCM(22, 33) by division method = 2 × 3 × 11 = 66.

☛ Also Check:

• LCM of 40, 48 and 45 - 720
• LCM of 10 and 24 - 120
• LCM of 7, 8, 14 and 21 - 168
• LCM of 48 and 56 - 336
• LCM of 45 and 90 - 90
• LCM of 5 and 15 - 15
• LCM of 36 and 45 - 180

FAQs on LCM of 22 and 33

What is the LCM of 22 and 33?

The LCM of 22 and 33 is 66. To find the least common multiple (LCM) of 22 and 33, we need to find the multiples of 22 and 33 (multiples of 22 = 22, 44, 66, 88; multiples of 33 = 33, 66, 99, 132) and choose the smallest multiple that is exactly divisible by 22 and 33, i.e., 66.

What is the Relation Between GCF and LCM of 22, 33?

The following equation can be used to express the relation between GCF and LCM of 22 and 33, i.e. GCF × LCM = 22 × 33.

How to Find the LCM of 22 and 33 by Prime Factorization?

To find the LCM of 22 and 33 using prime factorization, we will find the prime factors, (22 = 2 × 11) and (33 = 3 × 11). LCM of 22 and 33 is the product of prime factors raised to their respective highest exponent among the numbers 22 and 33.
⇒ LCM of 22, 33 = 2¹ × 3¹ × 11¹ = 66.

If the LCM of 33 and 22 is 66, Find its GCF.

LCM(33, 22) × GCF(33, 22) = 33 × 22
Since the LCM of 33 and 22 = 66
⇒ 66 × GCF(33, 22) = 726
Therefore, the GCF (greatest common factor) = 726/66 = 11.

What are the Methods to Find LCM of 22 and 33?

The commonly used methods to find the LCM of 22 and 33 are:

• Listing Multiples
• Division Method
• Prime Factorization Method