LCM of 7 and 20

LCM of 7 and 20 is the smallest number among all common multiples of 7 and 20. The first few multiples of 7 and 20 are (7, 14, 21, 28, . . . ) and (20, 40, 60, 80, 100, 120, 140, . . . ) respectively. There are 3 commonly used methods to find LCM of 7 and 20 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 7 and 20 is 140.

Explanation:

The LCM of two non-zero integers, x(7) and y(20), is the smallest positive integer m(140) that is divisible by both x(7) and y(20) without any remainder.

The methods to find the LCM of 7 and 20 are explained below.

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

LCM of 7 and 20 by Prime Factorization

Prime factorization of 7 and 20 is (7) = 7¹ and (2 × 2 × 5) = 2² × 5¹ respectively. LCM of 7 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 7 and 20 by prime factorization is 140.

LCM of 7 and 20 by Division Method

To calculate the LCM of 7 and 20 by the division method, we will divide the numbers(7, 20) by their prime factors (preferably common). The product of these divisors gives the LCM of 7 and 20.

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

LCM of 7 and 20 by Listing Multiples

To calculate the LCM of 7 and 20 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 7 (7, 14, 21, 28, . . . ) and 20 (20, 40, 60, 80, 100, 120, 140, . . . . )
• Step 2: The common multiples from the multiples of 7 and 20 are 140, 280, . . .
• Step 3: The smallest common multiple of 7 and 20 is 140.

∴ The least common multiple of 7 and 20 = 140.

☛ Also Check:

• LCM of 72 and 108 - 216
• LCM of 5, 9 and 15 - 45
• LCM of 12 and 28 - 84
• LCM of 24, 36 and 54 - 216
• LCM of 8 and 13 - 104
• LCM of 7 and 13 - 91
• LCM of 6, 12 and 18 - 36

FAQs on LCM of 7 and 20

What is the LCM of 7 and 20?

The LCM of 7 and 20 is 140. To find the least common multiple of 7 and 20, we need to find the multiples of 7 and 20 (multiples of 7 = 7, 14, 21, 28 . . . . 140; multiples of 20 = 20, 40, 60, 80 . . . . 140) and choose the smallest multiple that is exactly divisible by 7 and 20, i.e., 140.

What are the Methods to Find LCM of 7 and 20?

The commonly used methods to find the LCM of 7 and 20 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 20 and 7 is 140, Find its GCF.

LCM(20, 7) × GCF(20, 7) = 20 × 7
Since the LCM of 20 and 7 = 140
⇒ 140 × GCF(20, 7) = 140
Therefore, the GCF = 140/140 = 1.

What is the Relation Between GCF and LCM of 7, 20?

The following equation can be used to express the relation between GCF and LCM of 7 and 20, i.e. GCF × LCM = 7 × 20.

What is the Least Perfect Square Divisible by 7 and 20?

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