LCM of 14 and 91

LCM of 14 and 91 is the smallest number among all common multiples of 14 and 91. The first few multiples of 14 and 91 are (14, 28, 42, 56, 70, 84, . . . ) and (91, 182, 273, 364, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 91 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 14 and 91 is 182.

Explanation:

The LCM of two non-zero integers, x(14) and y(91), is the smallest positive integer m(182) that is divisible by both x(14) and y(91) without any remainder.

The methods to find the LCM of 14 and 91 are explained below.

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

LCM of 14 and 91 by Prime Factorization

Prime factorization of 14 and 91 is (2 × 7) = 2¹ × 7¹ and (7 × 13) = 7¹ × 13¹ respectively. LCM of 14 and 91 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 7¹ × 13¹ = 182.
Hence, the LCM of 14 and 91 by prime factorization is 182.

LCM of 14 and 91 by Listing Multiples

To calculate the LCM of 14 and 91 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, . . . ) and 91 (91, 182, 273, 364, . . . . )
• Step 2: The common multiples from the multiples of 14 and 91 are 182, 364, . . .
• Step 3: The smallest common multiple of 14 and 91 is 182.

∴ The least common multiple of 14 and 91 = 182.

LCM of 14 and 91 by Division Method

To calculate the LCM of 14 and 91 by the division method, we will divide the numbers(14, 91) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 91.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 91. Write this prime number(2) on the left of the given numbers(14 and 91), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 91) 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 91 is the product of all prime numbers on the left, i.e. LCM(14, 91) by division method = 2 × 7 × 13 = 182.

☛ Also Check:

• LCM of 50 and 48 - 1200
• LCM of 5 and 9 - 45
• LCM of 5 and 8 - 40
• LCM of 5 and 7 - 35
• LCM of 5 and 6 - 30
• LCM of 5 and 30 - 30
• LCM of 5 and 25 - 25

FAQs on LCM of 14 and 91

What is the LCM of 14 and 91?

The LCM of 14 and 91 is 182. To find the least common multiple (LCM) of 14 and 91, we need to find the multiples of 14 and 91 (multiples of 14 = 14, 28, 42, 56 . . . . 182; multiples of 91 = 91, 182, 273, 364) and choose the smallest multiple that is exactly divisible by 14 and 91, i.e., 182.

What are the Methods to Find LCM of 14 and 91?

The commonly used methods to find the LCM of 14 and 91 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

What is the Least Perfect Square Divisible by 14 and 91?

The least number divisible by 14 and 91 = LCM(14, 91)
LCM of 14 and 91 = 2 × 7 × 13 [Incomplete pair(s): 2, 7, 13]
⇒ Least perfect square divisible by each 14 and 91 = LCM(14, 91) × 2 × 7 × 13 = 33124 [Square root of 33124 = √33124 = ±182]
Therefore, 33124 is the required number.

If the LCM of 91 and 14 is 182, Find its GCF.

LCM(91, 14) × GCF(91, 14) = 91 × 14
Since the LCM of 91 and 14 = 182
⇒ 182 × GCF(91, 14) = 1274
Therefore, the GCF (greatest common factor) = 1274/182 = 7.

How to Find the LCM of 14 and 91 by Prime Factorization?

To find the LCM of 14 and 91 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (91 = 7 × 13). LCM of 14 and 91 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 91.
⇒ LCM of 14, 91 = 2¹ × 7¹ × 13¹ = 182.