LCM of 6 and 19

LCM of 6 and 19 is the smallest number among all common multiples of 6 and 19. The first few multiples of 6 and 19 are (6, 12, 18, 24, . . . ) and (19, 38, 57, 76, 95, 114, 133, . . . ) respectively. There are 3 commonly used methods to find LCM of 6 and 19 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 6 and 19 is 114.

Explanation:

The LCM of two non-zero integers, x(6) and y(19), is the smallest positive integer m(114) that is divisible by both x(6) and y(19) without any remainder.

Let's look at the different methods for finding the LCM of 6 and 19.

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

LCM of 6 and 19 by Division Method

To calculate the LCM of 6 and 19 by the division method, we will divide the numbers(6, 19) by their prime factors (preferably common). The product of these divisors gives the LCM of 6 and 19.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 6 and 19. Write this prime number(2) on the left of the given numbers(6 and 19), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (6, 19) 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 19 is the product of all prime numbers on the left, i.e. LCM(6, 19) by division method = 2 × 3 × 19 = 114.

LCM of 6 and 19 by Listing Multiples

To calculate the LCM of 6 and 19 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, . . . ) and 19 (19, 38, 57, 76, 95, 114, 133, . . . . )
• Step 2: The common multiples from the multiples of 6 and 19 are 114, 228, . . .
• Step 3: The smallest common multiple of 6 and 19 is 114.

∴ The least common multiple of 6 and 19 = 114.

LCM of 6 and 19 by Prime Factorization

Prime factorization of 6 and 19 is (2 × 3) = 2¹ × 3¹ and (19) = 19¹ respectively. LCM of 6 and 19 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 19¹ = 114.
Hence, the LCM of 6 and 19 by prime factorization is 114.

☛ Also Check:

• LCM of 12 and 24 - 24
• LCM of 23 and 69 - 69
• LCM of 8, 9 and 12 - 72
• LCM of 4, 12 and 20 - 60
• LCM of 12 and 45 - 180
• LCM of 15 and 30 - 30
• LCM of 11 and 15 - 165

FAQs on LCM of 6 and 19

What is the LCM of 6 and 19?

The LCM of 6 and 19 is 114. To find the LCM (least common multiple) of 6 and 19, we need to find the multiples of 6 and 19 (multiples of 6 = 6, 12, 18, 24 . . . . 114; multiples of 19 = 19, 38, 57, 76 . . . . 114) and choose the smallest multiple that is exactly divisible by 6 and 19, i.e., 114.

If the LCM of 19 and 6 is 114, Find its GCF.

LCM(19, 6) × GCF(19, 6) = 19 × 6
Since the LCM of 19 and 6 = 114
⇒ 114 × GCF(19, 6) = 114
Therefore, the greatest common factor (GCF) = 114/114 = 1.

Which of the following is the LCM of 6 and 19? 40, 50, 114, 28

The value of LCM of 6, 19 is the smallest common multiple of 6 and 19. The number satisfying the given condition is 114.

What is the Relation Between GCF and LCM of 6, 19?

The following equation can be used to express the relation between GCF and LCM of 6 and 19, i.e. GCF × LCM = 6 × 19.

How to Find the LCM of 6 and 19 by Prime Factorization?

To find the LCM of 6 and 19 using prime factorization, we will find the prime factors, (6 = 2 × 3) and (19 = 19). LCM of 6 and 19 is the product of prime factors raised to their respective highest exponent among the numbers 6 and 19.
⇒ LCM of 6, 19 = 2¹ × 3¹ × 19¹ = 114.