LCM of 30 and 45

LCM of 30 and 45 is the smallest number among all common multiples of 30 and 45. The first few multiples of 30 and 45 are (30, 60, 90, 120, 150, . . . ) and (45, 90, 135, 180, . . . ) respectively. There are 3 commonly used methods to find LCM of 30 and 45 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 30 and 45 is 90.

Explanation:

The LCM of two non-zero integers, x(30) and y(45), is the smallest positive integer m(90) that is divisible by both x(30) and y(45) without any remainder.

Let's look at the different methods for finding the LCM of 30 and 45.

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

LCM of 30 and 45 by Listing Multiples

To calculate the LCM of 30 and 45 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, . . . ) and 45 (45, 90, 135, 180, . . . . )
• Step 2: The common multiples from the multiples of 30 and 45 are 90, 180, . . .
• Step 3: The smallest common multiple of 30 and 45 is 90.

∴ The least common multiple of 30 and 45 = 90.

LCM of 30 and 45 by Prime Factorization

Prime factorization of 30 and 45 is (2 × 3 × 5) = 2¹ × 3¹ × 5¹ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 30 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ = 90.
Hence, the LCM of 30 and 45 by prime factorization is 90.

LCM of 30 and 45 by Division Method

To calculate the LCM of 30 and 45 by the division method, we will divide the numbers(30, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 30 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 30 and 45. Write this prime number(2) on the left of the given numbers(30 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (30, 45) 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 45 is the product of all prime numbers on the left, i.e. LCM(30, 45) by division method = 2 × 3 × 3 × 5 = 90.

☛ Also Check:

• LCM of 3, 5 and 6 - 30
• LCM of 20 and 50 - 100
• LCM of 2 and 11 - 22
• LCM of 12 and 18 - 36
• LCM of 7 and 13 - 91
• LCM of 45 and 86 - 3870
• LCM of 7 and 9 - 63

FAQs on LCM of 30 and 45

What is the LCM of 30 and 45?

The LCM of 30 and 45 is 90. To find the least common multiple of 30 and 45, we need to find the multiples of 30 and 45 (multiples of 30 = 30, 60, 90, 120; multiples of 45 = 45, 90, 135, 180) and choose the smallest multiple that is exactly divisible by 30 and 45, i.e., 90.

Which of the following is the LCM of 30 and 45? 50, 21, 90, 45

The value of LCM of 30, 45 is the smallest common multiple of 30 and 45. The number satisfying the given condition is 90.

What are the Methods to Find LCM of 30 and 45?

The commonly used methods to find the LCM of 30 and 45 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

How to Find the LCM of 30 and 45 by Prime Factorization?

To find the LCM of 30 and 45 using prime factorization, we will find the prime factors, (30 = 2 × 3 × 5) and (45 = 3 × 3 × 5). LCM of 30 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 30 and 45.
⇒ LCM of 30, 45 = 2¹ × 3² × 5¹ = 90.

If the LCM of 45 and 30 is 90, Find its GCF.

LCM(45, 30) × GCF(45, 30) = 45 × 30
Since the LCM of 45 and 30 = 90
⇒ 90 × GCF(45, 30) = 1350
Therefore, the GCF (greatest common factor) = 1350/90 = 15.