LCM of 32 and 36

LCM of 32 and 36 is the smallest number among all common multiples of 32 and 36. The first few multiples of 32 and 36 are (32, 64, 96, 128, 160, 192, 224, . . . ) and (36, 72, 108, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 32 and 36 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 32 and 36 is 288.

Explanation:

The LCM of two non-zero integers, x(32) and y(36), is the smallest positive integer m(288) that is divisible by both x(32) and y(36) without any remainder.

The methods to find the LCM of 32 and 36 are explained below.

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

LCM of 32 and 36 by Prime Factorization

Prime factorization of 32 and 36 is (2 × 2 × 2 × 2 × 2) = 2⁵ and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 32 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 3² = 288.
Hence, the LCM of 32 and 36 by prime factorization is 288.

LCM of 32 and 36 by Listing Multiples

To calculate the LCM of 32 and 36 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, 192, 224, . . . ) and 36 (36, 72, 108, 144, . . . . )
• Step 2: The common multiples from the multiples of 32 and 36 are 288, 576, . . .
• Step 3: The smallest common multiple of 32 and 36 is 288.

∴ The least common multiple of 32 and 36 = 288.

LCM of 32 and 36 by Division Method

To calculate the LCM of 32 and 36 by the division method, we will divide the numbers(32, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 32 and 36.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 32 and 36. Write this prime number(2) on the left of the given numbers(32 and 36), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (32, 36) 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 36 is the product of all prime numbers on the left, i.e. LCM(32, 36) by division method = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.

☛ Also Check:

• LCM of 2, 4, 6 and 8 - 24
• LCM of 8, 12 and 18 - 72
• LCM of 10 and 30 - 30
• LCM of 30 and 45 - 90
• LCM of 72 and 84 - 504
• LCM of 7, 8, 14 and 21 - 168
• LCM of 4, 7 and 14 - 28

FAQs on LCM of 32 and 36

What is the LCM of 32 and 36?

The LCM of 32 and 36 is 288. To find the least common multiple (LCM) of 32 and 36, we need to find the multiples of 32 and 36 (multiples of 32 = 32, 64, 96, 128 . . . . 288; multiples of 36 = 36, 72, 108, 144 . . . . 288) and choose the smallest multiple that is exactly divisible by 32 and 36, i.e., 288.

If the LCM of 36 and 32 is 288, Find its GCF.

LCM(36, 32) × GCF(36, 32) = 36 × 32
Since the LCM of 36 and 32 = 288
⇒ 288 × GCF(36, 32) = 1152
Therefore, the greatest common factor (GCF) = 1152/288 = 4.

Which of the following is the LCM of 32 and 36? 16, 288, 50, 40

The value of LCM of 32, 36 is the smallest common multiple of 32 and 36. The number satisfying the given condition is 288.

How to Find the LCM of 32 and 36 by Prime Factorization?

To find the LCM of 32 and 36 using prime factorization, we will find the prime factors, (32 = 2 × 2 × 2 × 2 × 2) and (36 = 2 × 2 × 3 × 3). LCM of 32 and 36 is the product of prime factors raised to their respective highest exponent among the numbers 32 and 36.
⇒ LCM of 32, 36 = 2⁵ × 3² = 288.

What are the Methods to Find LCM of 32 and 36?

The commonly used methods to find the LCM of 32 and 36 are:

• Division Method
• Prime Factorization Method
• Listing Multiples