LCM of 14 and 122

LCM of 14 and 122 is the smallest number among all common multiples of 14 and 122. The first few multiples of 14 and 122 are (14, 28, 42, 56, 70, 84, 98, . . . ) and (122, 244, 366, 488, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 122 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 14 and 122 is 854.

Explanation:

The LCM of two non-zero integers, x(14) and y(122), is the smallest positive integer m(854) that is divisible by both x(14) and y(122) without any remainder.

Let's look at the different methods for finding the LCM of 14 and 122.

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

LCM of 14 and 122 by Division Method

To calculate the LCM of 14 and 122 by the division method, we will divide the numbers(14, 122) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 122.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 122. Write this prime number(2) on the left of the given numbers(14 and 122), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 122) 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 14 and 122 is the product of all prime numbers on the left, i.e. LCM(14, 122) by division method = 2 × 7 × 61 = 854.

LCM of 14 and 122 by Listing Multiples

To calculate the LCM of 14 and 122 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 14 (14, 28, 42, 56, 70, 84, 98, . . . ) and 122 (122, 244, 366, 488, . . . . )
• Step 2: The common multiples from the multiples of 14 and 122 are 854, 1708, . . .
• Step 3: The smallest common multiple of 14 and 122 is 854.

∴ The least common multiple of 14 and 122 = 854.

LCM of 14 and 122 by Prime Factorization

Prime factorization of 14 and 122 is (2 × 7) = 2¹ × 7¹ and (2 × 61) = 2¹ × 61¹ respectively. LCM of 14 and 122 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 7¹ × 61¹ = 854.
Hence, the LCM of 14 and 122 by prime factorization is 854.

☛ Also Check:

• LCM of 3, 6, 9 and 12 - 36
• LCM of 3, 4, 5 and 6 - 60
• LCM of 28, 36, 45 and 60 - 1260
• LCM of 24, 36, 44 and 62 - 24552
• LCM of 21, 28, 36 and 45 - 1260
• LCM of 2, 4, 6 and 8 - 24
• LCM of 2, 3, 4 and 5 - 60

FAQs on LCM of 14 and 122

What is the LCM of 14 and 122?

The LCM of 14 and 122 is 854. To find the LCM (least common multiple) of 14 and 122, we need to find the multiples of 14 and 122 (multiples of 14 = 14, 28, 42, 56 . . . . 854; multiples of 122 = 122, 244, 366, 488 . . . . 854) and choose the smallest multiple that is exactly divisible by 14 and 122, i.e., 854.

If the LCM of 122 and 14 is 854, Find its GCF.

LCM(122, 14) × GCF(122, 14) = 122 × 14
Since the LCM of 122 and 14 = 854
⇒ 854 × GCF(122, 14) = 1708
Therefore, the GCF (greatest common factor) = 1708/854 = 2.

What is the Relation Between GCF and LCM of 14, 122?

The following equation can be used to express the relation between GCF and LCM of 14 and 122, i.e. GCF × LCM = 14 × 122.

What are the Methods to Find LCM of 14 and 122?

The commonly used methods to find the LCM of 14 and 122 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

Which of the following is the LCM of 14 and 122? 10, 27, 32, 854

The value of LCM of 14, 122 is the smallest common multiple of 14 and 122. The number satisfying the given condition is 854.