LCM of 32 and 45

LCM of 32 and 45 is the smallest number among all common multiples of 32 and 45. The first few multiples of 32 and 45 are (32, 64, 96, 128, . . . ) and (45, 90, 135, 180, 225, 270, . . . ) respectively. There are 3 commonly used methods to find LCM of 32 and 45 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 32 and 45 is 1440.

Explanation:

The LCM of two non-zero integers, x(32) and y(45), is the smallest positive integer m(1440) that is divisible by both x(32) and y(45) without any remainder.

Let's look at the different methods for finding the LCM of 32 and 45.

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

LCM of 32 and 45 by Division Method

To calculate the LCM of 32 and 45 by the division method, we will divide the numbers(32, 45) by their prime factors (preferably common). The product of these divisors gives the LCM of 32 and 45.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 32 and 45. Write this prime number(2) on the left of the given numbers(32 and 45), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (32, 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 32 and 45 is the product of all prime numbers on the left, i.e. LCM(32, 45) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 5 = 1440.

LCM of 32 and 45 by Listing Multiples

To calculate the LCM of 32 and 45 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 32 (32, 64, 96, 128, . . . ) and 45 (45, 90, 135, 180, 225, 270, . . . . )
• Step 2: The common multiples from the multiples of 32 and 45 are 1440, 2880, . . .
• Step 3: The smallest common multiple of 32 and 45 is 1440.

∴ The least common multiple of 32 and 45 = 1440.

LCM of 32 and 45 by Prime Factorization

Prime factorization of 32 and 45 is (2 × 2 × 2 × 2 × 2) = 2⁵ and (3 × 3 × 5) = 3² × 5¹ respectively. LCM of 32 and 45 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 3² × 5¹ = 1440.
Hence, the LCM of 32 and 45 by prime factorization is 1440.

☛ Also Check:

• LCM of 13 and 91 - 91
• LCM of 60 and 90 - 180
• LCM of 8 and 36 - 72
• LCM of 24, 36, 44 and 62 - 24552
• LCM of 72 and 24 - 72
• LCM of 14 and 56 - 56
• LCM of 9 and 10 - 90

FAQs on LCM of 32 and 45

What is the LCM of 32 and 45?

The LCM of 32 and 45 is 1440. To find the LCM of 32 and 45, we need to find the multiples of 32 and 45 (multiples of 32 = 32, 64, 96, 128 . . . . 1440; multiples of 45 = 45, 90, 135, 180 . . . . 1440) and choose the smallest multiple that is exactly divisible by 32 and 45, i.e., 1440.

If the LCM of 45 and 32 is 1440, Find its GCF.

LCM(45, 32) × GCF(45, 32) = 45 × 32
Since the LCM of 45 and 32 = 1440
⇒ 1440 × GCF(45, 32) = 1440
Therefore, the GCF = 1440/1440 = 1.

Which of the following is the LCM of 32 and 45? 2, 25, 18, 1440

The value of LCM of 32, 45 is the smallest common multiple of 32 and 45. The number satisfying the given condition is 1440.

What are the Methods to Find LCM of 32 and 45?

The commonly used methods to find the LCM of 32 and 45 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

How to Find the LCM of 32 and 45 by Prime Factorization?

To find the LCM of 32 and 45 using prime factorization, we will find the prime factors, (32 = 2 × 2 × 2 × 2 × 2) and (45 = 3 × 3 × 5). LCM of 32 and 45 is the product of prime factors raised to their respective highest exponent among the numbers 32 and 45.
⇒ LCM of 32, 45 = 2⁵ × 3² × 5¹ = 1440.