LCM of 30 and 75

LCM of 30 and 75 is the smallest number among all common multiples of 30 and 75. The first few multiples of 30 and 75 are (30, 60, 90, 120, 150, 180, 210, . . . ) and (75, 150, 225, 300, 375, 450, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 75 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 30 and 75 is 150.

Explanation:

The LCM of two non-zero integers, x(30) and y(75), is the smallest positive integer m(150) that is divisible by both x(30) and y(75) without any remainder.

Let's look at the different methods for finding the LCM of 30 and 75.

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

LCM of 30 and 75 by Division Method

To calculate the LCM of 30 and 75 by the division method, we will divide the numbers(30, 75) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 75.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 75. Write this prime number(2) on the left of the given numbers(30 and 75), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (30, 75) 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 75 is the product of all prime numbers on the left, i.e. LCM(30, 75) by division method = 2 × 3 × 5 × 5 = 150.

LCM of 30 and 75 by Listing Multiples

To calculate the LCM of 30 and 75 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, 150, 180, 210, . . . ) and 75 (75, 150, 225, 300, 375, 450, . . . . )
• Step 2: The common multiples from the multiples of 30 and 75 are 150, 300, . . .
• Step 3: The smallest common multiple of 30 and 75 is 150.

∴ The least common multiple of 30 and 75 = 150.

LCM of 30 and 75 by Prime Factorization

Prime factorization of 30 and 75 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (3 × 5 × 5) = 3¹ × 5² respectively. LCM of 30 and 75 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 75 by prime factorization is 150.

☛ Also Check:

• LCM of 2 and 13 - 26
• LCM of 5, 8 and 15 - 120
• LCM of 25 and 100 - 100
• LCM of 5 and 14 - 70
• LCM of 20 and 30 - 60
• LCM of 5, 6 and 7 - 210
• LCM of 50 and 75 - 150

FAQs on LCM of 30 and 75

What is the LCM of 30 and 75?

The LCM of 30 and 75 is 150. To find the LCM of 30 and 75, we need to find the multiples of 30 and 75 (multiples of 30 = 30, 60, 90, 120 . . . . 150; multiples of 75 = 75, 150, 225, 300) and choose the smallest multiple that is exactly divisible by 30 and 75, i.e., 150.

How to Find the LCM of 30 and 75 by Prime Factorization?

To find the LCM of 30 and 75 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (75 = 3 × 5 × 5). LCM of 30 and 75 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 75.
⇒ LCM of 30, 75 = 2¹ × 3¹ × 5² = 150.

What are the Methods to Find LCM of 30 and 75?

The commonly used methods to find the LCM of 30 and 75 are:

• Listing Multiples
• Prime Factorization Method
• Division Method

If the LCM of 75 and 30 is 150, Find its GCF.

LCM(75, 30) × GCF(75, 30) = 75 × 30
Since the LCM of 75 and 30 = 150
⇒ 150 × GCF(75, 30) = 2250
Therefore, the GCF = 2250/150 = 15.

Which of the following is the LCM of 30 and 75? 150, 42, 20, 27

The value of LCM of 30, 75 is the smallest common multiple of 30 and 75. The number satisfying the given condition is 150.