LCM of 32 and 37

LCM of 32 and 37 is the smallest number among all common multiples of 32 and 37. The first few multiples of 32 and 37 are (32, 64, 96, 128, 160, . . . ) and (37, 74, 111, 148, 185, 222, . . . ) respectively. There are 3 commonly used methods to find LCM of 32 and 37 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 32 and 37 is 1184.

Explanation:

The LCM of two non-zero integers, x(32) and y(37), is the smallest positive integer m(1184) that is divisible by both x(32) and y(37) without any remainder.

The methods to find the LCM of 32 and 37 are explained below.

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

LCM of 32 and 37 by Division Method

To calculate the LCM of 32 and 37 by the division method, we will divide the numbers(32, 37) by their prime factors (preferably common). The product of these divisors gives the LCM of 32 and 37.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 32 and 37. Write this prime number(2) on the left of the given numbers(32 and 37), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (32, 37) 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 37 is the product of all prime numbers on the left, i.e. LCM(32, 37) by division method = 2 × 2 × 2 × 2 × 2 × 37 = 1184.

LCM of 32 and 37 by Prime Factorization

Prime factorization of 32 and 37 is (2 × 2 × 2 × 2 × 2) = 2⁵ and (37) = 37¹ respectively. LCM of 32 and 37 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 37¹ = 1184.
Hence, the LCM of 32 and 37 by prime factorization is 1184.

LCM of 32 and 37 by Listing Multiples

To calculate the LCM of 32 and 37 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, 160, . . . ) and 37 (37, 74, 111, 148, 185, 222, . . . . )
• Step 2: The common multiples from the multiples of 32 and 37 are 1184, 2368, . . .
• Step 3: The smallest common multiple of 32 and 37 is 1184.

∴ The least common multiple of 32 and 37 = 1184.

☛ Also Check:

• LCM of 30 and 40 - 120
• LCM of 80 and 120 - 240
• LCM of 12, 15 and 20 - 60
• LCM of 3 and 4 - 12
• LCM of 18 and 20 - 180
• LCM of 35 and 70 - 70
• LCM of 10 and 100 - 100

FAQs on LCM of 32 and 37

What is the LCM of 32 and 37?

The LCM of 32 and 37 is 1184. To find the least common multiple of 32 and 37, we need to find the multiples of 32 and 37 (multiples of 32 = 32, 64, 96, 128 . . . . 1184; multiples of 37 = 37, 74, 111, 148 . . . . 1184) and choose the smallest multiple that is exactly divisible by 32 and 37, i.e., 1184.

How to Find the LCM of 32 and 37 by Prime Factorization?

To find the LCM of 32 and 37 using prime factorization, we will find the prime factors, (32 = 2 × 2 × 2 × 2 × 2) and (37 = 37). LCM of 32 and 37 is the product of prime factors raised to their respective highest exponent among the numbers 32 and 37.
⇒ LCM of 32, 37 = 2⁵ × 37¹ = 1184.

If the LCM of 37 and 32 is 1184, Find its GCF.

LCM(37, 32) × GCF(37, 32) = 37 × 32
Since the LCM of 37 and 32 = 1184
⇒ 1184 × GCF(37, 32) = 1184
Therefore, the GCF (greatest common factor) = 1184/1184 = 1.

What is the Least Perfect Square Divisible by 32 and 37?

The least number divisible by 32 and 37 = LCM(32, 37)
LCM of 32 and 37 = 2 × 2 × 2 × 2 × 2 × 37 [Incomplete pair(s): 2, 37]
⇒ Least perfect square divisible by each 32 and 37 = LCM(32, 37) × 2 × 37 = 87616 [Square root of 87616 = √87616 = ±296]
Therefore, 87616 is the required number.

What are the Methods to Find LCM of 32 and 37?

The commonly used methods to find the LCM of 32 and 37 are:

• Listing Multiples
• Division Method
• Prime Factorization Method