LCM of 8 and 30

LCM of 8 and 30 is the smallest number among all common multiples of 8 and 30. The first few multiples of 8 and 30 are (8, 16, 24, 32, . . . ) and (30, 60, 90, 120, 150, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 30 - by division method, by listing multiples, and by prime factorization.

Answer: LCM of 8 and 30 is 120.

Explanation:

The LCM of two non-zero integers, x(8) and y(30), is the smallest positive integer m(120) that is divisible by both x(8) and y(30) without any remainder.

Let's look at the different methods for finding the LCM of 8 and 30.

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

LCM of 8 and 30 by Prime Factorization

Prime factorization of 8 and 30 is (2 × 2 × 2) = 2³ and (2 × 3 × 5) = 2¹ × 3¹ × 5¹ respectively. LCM of 8 and 30 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 5¹ = 120.
Hence, the LCM of 8 and 30 by prime factorization is 120.

LCM of 8 and 30 by Division Method

To calculate the LCM of 8 and 30 by the division method, we will divide the numbers(8, 30) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 30.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 30. Write this prime number(2) on the left of the given numbers(8 and 30), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 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 8 and 30 is the product of all prime numbers on the left, i.e. LCM(8, 30) by division method = 2 × 2 × 2 × 3 × 5 = 120.

LCM of 8 and 30 by Listing Multiples

To calculate the LCM of 8 and 30 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, . . . ) and 30 (30, 60, 90, 120, 150, 180, . . . . )
• Step 2: The common multiples from the multiples of 8 and 30 are 120, 240, . . .
• Step 3: The smallest common multiple of 8 and 30 is 120.

∴ The least common multiple of 8 and 30 = 120.

☛ Also Check:

• LCM of 10, 15 and 20 - 60
• LCM of 150 and 180 - 900
• LCM of 56 and 84 - 168
• LCM of 30 and 42 - 210
• LCM of 10, 20 and 25 - 100
• LCM of 60, 84 and 108 - 3780
• LCM of 3 and 15 - 15

FAQs on LCM of 8 and 30

What is the LCM of 8 and 30?

The LCM of 8 and 30 is 120. To find the least common multiple of 8 and 30, we need to find the multiples of 8 and 30 (multiples of 8 = 8, 16, 24, 32 . . . . 120; multiples of 30 = 30, 60, 90, 120) and choose the smallest multiple that is exactly divisible by 8 and 30, i.e., 120.

What are the Methods to Find LCM of 8 and 30?

The commonly used methods to find the LCM of 8 and 30 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

What is the Relation Between GCF and LCM of 8, 30?

The following equation can be used to express the relation between GCF and LCM of 8 and 30, i.e. GCF × LCM = 8 × 30.

If the LCM of 30 and 8 is 120, Find its GCF.

LCM(30, 8) × GCF(30, 8) = 30 × 8
Since the LCM of 30 and 8 = 120
⇒ 120 × GCF(30, 8) = 240
Therefore, the greatest common factor (GCF) = 240/120 = 2.

How to Find the LCM of 8 and 30 by Prime Factorization?

To find the LCM of 8 and 30 using prime factorization, we will find the prime factors, (8 = 2 × 2 × 2) and (30 = 2 × 3 × 5). LCM of 8 and 30 is the product of prime factors raised to their respective highest exponent among the numbers 8 and 30.
⇒ LCM of 8, 30 = 2³ × 3¹ × 5¹ = 120.