LCM of 2 and 30

LCM of 2 and 30 is the smallest number among all common multiples of 2 and 30. The first few multiples of 2 and 30 are (2, 4, 6, 8, 10, 12, 14, . . . ) and (30, 60, 90, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 2 and 30 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 2 and 30 is 30.

Explanation:

The LCM of two non-zero integers, x(2) and y(30), is the smallest positive integer m(30) that is divisible by both x(2) and y(30) without any remainder.

The methods to find the LCM of 2 and 30 are explained below.

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

LCM of 2 and 30 by Listing Multiples

To calculate the LCM of 2 and 30 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 2 (2, 4, 6, 8, 10, 12, 14, . . . ) and 30 (30, 60, 90, 120, . . . . )
• Step 2: The common multiples from the multiples of 2 and 30 are 30, 60, . . .
• Step 3: The smallest common multiple of 2 and 30 is 30.

∴ The least common multiple of 2 and 30 = 30.

LCM of 2 and 30 by Prime Factorization

Prime factorization of 2 and 30 is (2) = 2¹ and (2 × 3 × 5) = 2¹ × 3¹ × 5¹ respectively. LCM of 2 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5¹ = 30.
Hence, the LCM of 2 and 30 by prime factorization is 30.

LCM of 2 and 30 by Division Method

To calculate the LCM of 2 and 30 by the division method, we will divide the numbers(2, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 2 and 30.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 2 and 30. Write this prime number(2) on the left of the given numbers(2 and 30), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (2, 30) 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 2 and 30 is the product of all prime numbers on the left, i.e. LCM(2, 30) by division method = 2 × 3 × 5 = 30.

☛ Also Check:

• LCM of 28 and 42 - 84
• LCM of 10 and 50 - 50
• LCM of 60 and 75 - 300
• LCM of 45 and 90 - 90
• LCM of 6 and 7 - 42
• LCM of 4, 7 and 10 - 140
• LCM of 7 and 8 - 56

FAQs on LCM of 2 and 30

What is the LCM of 2 and 30?

The LCM of 2 and 30 is 30. To find the LCM of 2 and 30, we need to find the multiples of 2 and 30 (multiples of 2 = 2, 4, 6, 8 . . . . 30; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 2 and 30, i.e., 30.

What is the Relation Between GCF and LCM of 2, 30?

The following equation can be used to express the relation between GCF and LCM of 2 and 30, i.e. GCF × LCM = 2 × 30.

How to Find the LCM of 2 and 30 by Prime Factorization?

To find the LCM of 2 and 30 using prime factorization, we will find the prime factors, (2 = 2) and (30 = 2 × 3 × 5). LCM of 2 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 2 and 30.
⇒ LCM of 2, 30 = 2¹ × 3¹ × 5¹ = 30.

What are the Methods to Find LCM of 2 and 30?

The commonly used methods to find the LCM of 2 and 30 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

If the LCM of 30 and 2 is 30, Find its GCF.

LCM(30, 2) × GCF(30, 2) = 30 × 2
Since the LCM of 30 and 2 = 30
⇒ 30 × GCF(30, 2) = 60
Therefore, the greatest common factor (GCF) = 60/30 = 2.