LCM of 20 and 21

LCM of 20 and 21 is the smallest number among all common multiples of 20 and 21. The first few multiples of 20 and 21 are (20, 40, 60, 80, 100, . . . ) and (21, 42, 63, 84, 105, 126, 147, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 21 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 20 and 21 is 420.

Explanation:

The LCM of two non-zero integers, x(20) and y(21), is the smallest positive integer m(420) that is divisible by both x(20) and y(21) without any remainder.

The methods to find the LCM of 20 and 21 are explained below.

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

LCM of 20 and 21 by Prime Factorization

Prime factorization of 20 and 21 is (2 × 2 × 5) = 2² × 5¹ and (3 × 7) = 3¹ × 7¹ respectively. LCM of 20 and 21 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 5¹ × 7¹ = 420.
Hence, the LCM of 20 and 21 by prime factorization is 420.

LCM of 20 and 21 by Division Method

To calculate the LCM of 20 and 21 by the division method, we will divide the numbers(20, 21) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 21.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 21. Write this prime number(2) on the left of the given numbers(20 and 21), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (20, 21) 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 20 and 21 is the product of all prime numbers on the left, i.e. LCM(20, 21) by division method = 2 × 2 × 3 × 5 × 7 = 420.

LCM of 20 and 21 by Listing Multiples

To calculate the LCM of 20 and 21 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 20 (20, 40, 60, 80, 100, . . . ) and 21 (21, 42, 63, 84, 105, 126, 147, . . . . )
• Step 2: The common multiples from the multiples of 20 and 21 are 420, 840, . . .
• Step 3: The smallest common multiple of 20 and 21 is 420.

∴ The least common multiple of 20 and 21 = 420.

☛ Also Check:

• LCM of 5, 15 and 20 - 60
• LCM of 5 and 13 - 65
• LCM of 4 and 6 - 12
• LCM of 54 and 90 - 270
• LCM of 8 and 9 - 72
• LCM of 24 and 30 - 120
• LCM of 56 and 98 - 392

FAQs on LCM of 20 and 21

What is the LCM of 20 and 21?

The LCM of 20 and 21 is 420. To find the least common multiple (LCM) of 20 and 21, we need to find the multiples of 20 and 21 (multiples of 20 = 20, 40, 60, 80 . . . . 420; multiples of 21 = 21, 42, 63, 84 . . . . 420) and choose the smallest multiple that is exactly divisible by 20 and 21, i.e., 420.

How to Find the LCM of 20 and 21 by Prime Factorization?

To find the LCM of 20 and 21 using prime factorization, we will find the prime factors, (20 = 2 × 2 × 5) and (21 = 3 × 7). LCM of 20 and 21 is the product of prime factors raised to their respective highest exponent among the numbers 20 and 21.
⇒ LCM of 20, 21 = 2² × 3¹ × 5¹ × 7¹ = 420.

What is the Relation Between GCF and LCM of 20, 21?

The following equation can be used to express the relation between GCF and LCM of 20 and 21, i.e. GCF × LCM = 20 × 21.

If the LCM of 21 and 20 is 420, Find its GCF.

LCM(21, 20) × GCF(21, 20) = 21 × 20
Since the LCM of 21 and 20 = 420
⇒ 420 × GCF(21, 20) = 420
Therefore, the greatest common factor = 420/420 = 1.

Which of the following is the LCM of 20 and 21? 45, 18, 20, 420

The value of LCM of 20, 21 is the smallest common multiple of 20 and 21. The number satisfying the given condition is 420.