LCM of 30 and 50

LCM of 30 and 50 is the smallest number among all common multiples of 30 and 50. The first few multiples of 30 and 50 are (30, 60, 90, 120, . . . ) and (50, 100, 150, 200, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 50 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 30 and 50 is 150.

Explanation:

The LCM of two non-zero integers, x(30) and y(50), is the smallest positive integer m(150) that is divisible by both x(30) and y(50) without any remainder.

The methods to find the LCM of 30 and 50 are explained below.

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

LCM of 30 and 50 by Division Method

To calculate the LCM of 30 and 50 by the division method, we will divide the numbers(30, 50) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 50.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 50. Write this prime number(2) on the left of the given numbers(30 and 50), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (30, 50) 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 30 and 50 is the product of all prime numbers on the left, i.e. LCM(30, 50) by division method = 2 × 3 × 5 × 5 = 150.

LCM of 30 and 50 by Listing Multiples

To calculate the LCM of 30 and 50 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 30 (30, 60, 90, 120, . . . ) and 50 (50, 100, 150, 200, . . . . )
• Step 2: The common multiples from the multiples of 30 and 50 are 150, 300, . . .
• Step 3: The smallest common multiple of 30 and 50 is 150.

∴ The least common multiple of 30 and 50 = 150.

LCM of 30 and 50 by Prime Factorization

Prime factorization of 30 and 50 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (2 × 5 × 5) = 2¹ × 5² respectively. LCM of 30 and 50 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3¹ × 5² = 150.
Hence, the LCM of 30 and 50 by prime factorization is 150.

☛ Also Check:

• LCM of 6, 8 and 10 - 120
• LCM of 12 and 15 - 60
• LCM of 5 and 10 - 10
• LCM of 20 and 60 - 60
• LCM of 4 and 5 - 20
• LCM of 25 and 30 - 150
• LCM of 3 and 9 - 9

FAQs on LCM of 30 and 50

What is the LCM of 30 and 50?

The LCM of 30 and 50 is 150. To find the least common multiple (LCM) of 30 and 50, we need to find the multiples of 30 and 50 (multiples of 30 = 30, 60, 90, 120 . . . . 150; multiples of 50 = 50, 100, 150, 200) and choose the smallest multiple that is exactly divisible by 30 and 50, i.e., 150.

How to Find the LCM of 30 and 50 by Prime Factorization?

To find the LCM of 30 and 50 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (50 = 2 × 5 × 5). LCM of 30 and 50 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 50.
⇒ LCM of 30, 50 = 2¹ × 3¹ × 5² = 150.

If the LCM of 50 and 30 is 150, Find its GCF.

LCM(50, 30) × GCF(50, 30) = 50 × 30
Since the LCM of 50 and 30 = 150
⇒ 150 × GCF(50, 30) = 1500
Therefore, the GCF (greatest common factor) = 1500/150 = 10.

What is the Relation Between GCF and LCM of 30, 50?

The following equation can be used to express the relation between GCF and LCM of 30 and 50, i.e. GCF × LCM = 30 × 50.

Which of the following is the LCM of 30 and 50? 150, 25, 12, 35

The value of LCM of 30, 50 is the smallest common multiple of 30 and 50. The number satisfying the given condition is 150.