LCM of 14 and 20

LCM of 14 and 20 is the smallest number among all common multiples of 14 and 20. The first few multiples of 14 and 20 are (14, 28, 42, 56, 70, . . . ) and (20, 40, 60, 80, . . . ) respectively. There are 3 commonly used methods to find LCM of 14 and 20 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 14 and 20 is 140.

Explanation:

The LCM of two non-zero integers, x(14) and y(20), is the smallest positive integer m(140) that is divisible by both x(14) and y(20) without any remainder.

The methods to find the LCM of 14 and 20 are explained below.

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

LCM of 14 and 20 by Listing Multiples

To calculate the LCM of 14 and 20 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, . . . ) and 20 (20, 40, 60, 80, . . . . )
• Step 2: The common multiples from the multiples of 14 and 20 are 140, 280, . . .
• Step 3: The smallest common multiple of 14 and 20 is 140.

∴ The least common multiple of 14 and 20 = 140.

LCM of 14 and 20 by Division Method

To calculate the LCM of 14 and 20 by the division method, we will divide the numbers(14, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 14 and 20.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 14 and 20. Write this prime number(2) on the left of the given numbers(14 and 20), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (14, 20) 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 20 is the product of all prime numbers on the left, i.e. LCM(14, 20) by division method = 2 × 2 × 5 × 7 = 140.

LCM of 14 and 20 by Prime Factorization

Prime factorization of 14 and 20 is (2 × 7) = 2¹ × 7¹ and (2 × 2 × 5) = 2² × 5¹ respectively. LCM of 14 and 20 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 5¹ × 7¹ = 140.
Hence, the LCM of 14 and 20 by prime factorization is 140.

☛ Also Check:

• LCM of 9 and 13 - 117
• LCM of 9 and 12 - 36
• LCM of 9 and 11 - 99
• LCM of 9 and 10 - 90
• LCM of 87 and 145 - 435
• LCM of 850 and 680 - 3400
• LCM of 84 and 90 - 1260

FAQs on LCM of 14 and 20

What is the LCM of 14 and 20?

The LCM of 14 and 20 is 140. To find the least common multiple of 14 and 20, we need to find the multiples of 14 and 20 (multiples of 14 = 14, 28, 42, 56 . . . . 140; multiples of 20 = 20, 40, 60, 80 . . . . 140) and choose the smallest multiple that is exactly divisible by 14 and 20, i.e., 140.

What is the Least Perfect Square Divisible by 14 and 20?

The least number divisible by 14 and 20 = LCM(14, 20)
LCM of 14 and 20 = 2 × 2 × 5 × 7 [Incomplete pair(s): 5, 7]
⇒ Least perfect square divisible by each 14 and 20 = LCM(14, 20) × 5 × 7 = 4900 [Square root of 4900 = √4900 = ±70]
Therefore, 4900 is the required number.

How to Find the LCM of 14 and 20 by Prime Factorization?

To find the LCM of 14 and 20 using prime factorization, we will find the prime factors, (14 = 2 × 7) and (20 = 2 × 2 × 5). LCM of 14 and 20 is the product of prime factors raised to their respective highest exponent among the numbers 14 and 20.
⇒ LCM of 14, 20 = 2² × 5¹ × 7¹ = 140.

If the LCM of 20 and 14 is 140, Find its GCF.

LCM(20, 14) × GCF(20, 14) = 20 × 14
Since the LCM of 20 and 14 = 140
⇒ 140 × GCF(20, 14) = 280
Therefore, the greatest common factor (GCF) = 280/140 = 2.

What are the Methods to Find LCM of 14 and 20?

The commonly used methods to find the LCM of 14 and 20 are:

• Prime Factorization Method
• Listing Multiples
• Division Method