LCM of 6 and 22

LCM of 6 and 22 is the smallest number among all common multiples of 6 and 22. The first few multiples of 6 and 22 are (6, 12, 18, 24, 30, 36, 42, . . . ) and (22, 44, 66, 88, 110, 132, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 22 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 6 and 22 is 66.

Explanation:

The LCM of two non-zero integers, x(6) and y(22), is the smallest positive integer m(66) that is divisible by both x(6) and y(22) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 22.

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

LCM of 6 and 22 by Listing Multiples

To calculate the LCM of 6 and 22 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 6 (6, 12, 18, 24, 30, 36, 42, . . . ) and 22 (22, 44, 66, 88, 110, 132, . . . . )
• Step 2: The common multiples from the multiples of 6 and 22 are 66, 132, . . .
• Step 3: The smallest common multiple of 6 and 22 is 66.

∴ The least common multiple of 6 and 22 = 66.

LCM of 6 and 22 by Division Method

To calculate the LCM of 6 and 22 by the division method, we will divide the numbers(6, 22) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 22.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 22. Write this prime number(2) on the left of the given numbers(6 and 22), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 22) 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 6 and 22 is the product of all prime numbers on the left, i.e. LCM(6, 22) by division method = 2 × 3 × 11 = 66.

LCM of 6 and 22 by Prime Factorization

Prime factorization of 6 and 22 is (2 × 3) = 2¹ × 3¹ and (2 × 11) = 2¹ × 11¹ respectively. LCM of 6 and 22 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 11¹ = 66.
Hence, the LCM of 6 and 22 by prime factorization is 66.

☛ Also Check:

• LCM of 6, 8 and 10 - 120
• LCM of 37 and 49 - 1813
• LCM of 8 and 32 - 32
• LCM of 6, 8 and 15 - 120
• LCM of 22 and 33 - 66
• LCM of 24 and 84 - 168
• LCM of 15 and 16 - 240

FAQs on LCM of 6 and 22

What is the LCM of 6 and 22?

The LCM of 6 and 22 is 66. To find the LCM of 6 and 22, we need to find the multiples of 6 and 22 (multiples of 6 = 6, 12, 18, 24 . . . . 66; multiples of 22 = 22, 44, 66, 88) and choose the smallest multiple that is exactly divisible by 6 and 22, i.e., 66.

How to Find the LCM of 6 and 22 by Prime Factorization?

To find the LCM of 6 and 22 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (22 = 2 × 11). LCM of 6 and 22 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 22.
⇒ LCM of 6, 22 = 2¹ × 3¹ × 11¹ = 66.

Which of the following is the LCM of 6 and 22? 16, 42, 66, 18

The value of LCM of 6, 22 is the smallest common multiple of 6 and 22. The number satisfying the given condition is 66.

What is the Least Perfect Square Divisible by 6 and 22?

The least number divisible by 6 and 22 = LCM(6, 22)
LCM of 6 and 22 = 2 × 3 × 11 [Incomplete pair(s): 2, 3, 11]
⇒ Least perfect square divisible by each 6 and 22 = LCM(6, 22) × 2 × 3 × 11 = 4356 [Square root of 4356 = √4356 = ±66]
Therefore, 4356 is the required number.

If the LCM of 22 and 6 is 66, Find its GCF.

LCM(22, 6) × GCF(22, 6) = 22 × 6
Since the LCM of 22 and 6 = 66
⇒ 66 × GCF(22, 6) = 132
Therefore, the greatest common factor (GCF) = 132/66 = 2.