LCM of 20 and 32

LCM of 20 and 32 is the smallest number among all common multiples of 20 and 32. The first few multiples of 20 and 32 are (20, 40, 60, 80, 100, 120, 140, . . . ) and (32, 64, 96, 128, 160, . . . ) respectively. There are 3 commonly used methods to find LCM of 20 and 32 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 20 and 32 is 160.

Explanation:

The LCM of two non-zero integers, x(20) and y(32), is the smallest positive integer m(160) that is divisible by both x(20) and y(32) without any remainder.

Let's look at the different methods for finding the LCM of 20 and 32.

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

LCM of 20 and 32 by Prime Factorization

Prime factorization of 20 and 32 is (2 × 2 × 5) = 2² × 5¹ and (2 × 2 × 2 × 2 × 2) = 2⁵ respectively. LCM of 20 and 32 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁵ × 5¹ = 160.
Hence, the LCM of 20 and 32 by prime factorization is 160.

LCM of 20 and 32 by Division Method

To calculate the LCM of 20 and 32 by the division method, we will divide the numbers(20, 32) by their prime factors (preferably common). The product of these divisors gives the LCM of 20 and 32.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 20 and 32. Write this prime number(2) on the left of the given numbers(20 and 32), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (20, 32) 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 20 and 32 is the product of all prime numbers on the left, i.e. LCM(20, 32) by division method = 2 × 2 × 2 × 2 × 2 × 5 = 160.

LCM of 20 and 32 by Listing Multiples

To calculate the LCM of 20 and 32 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 20 (20, 40, 60, 80, 100, 120, 140, . . . ) and 32 (32, 64, 96, 128, 160, . . . . )
• Step 2: The common multiples from the multiples of 20 and 32 are 160, 320, . . .
• Step 3: The smallest common multiple of 20 and 32 is 160.

∴ The least common multiple of 20 and 32 = 160.

☛ Also Check:

• LCM of 20 and 30 - 60
• LCM of 8 and 15 - 120
• LCM of 26 and 169 - 338
• LCM of 18 and 17 - 306
• LCM of 5 and 6 - 30
• LCM of 24 and 48 - 48
• LCM of 15 and 17 - 255

FAQs on LCM of 20 and 32

What is the LCM of 20 and 32?

The LCM of 20 and 32 is 160. To find the LCM of 20 and 32, we need to find the multiples of 20 and 32 (multiples of 20 = 20, 40, 60, 80 . . . . 160; multiples of 32 = 32, 64, 96, 128 . . . . 160) and choose the smallest multiple that is exactly divisible by 20 and 32, i.e., 160.

If the LCM of 32 and 20 is 160, Find its GCF.

LCM(32, 20) × GCF(32, 20) = 32 × 20
Since the LCM of 32 and 20 = 160
⇒ 160 × GCF(32, 20) = 640
Therefore, the GCF = 640/160 = 4.

What is the Least Perfect Square Divisible by 20 and 32?

The least number divisible by 20 and 32 = LCM(20, 32)
LCM of 20 and 32 = 2 × 2 × 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 20 and 32 = LCM(20, 32) × 2 × 5 = 1600 [Square root of 1600 = √1600 = ±40]
Therefore, 1600 is the required number.

What is the Relation Between GCF and LCM of 20, 32?

The following equation can be used to express the relation between GCF and LCM of 20 and 32, i.e. GCF × LCM = 20 × 32.

Which of the following is the LCM of 20 and 32? 40, 160, 35, 5

The value of LCM of 20, 32 is the smallest common multiple of 20 and 32. The number satisfying the given condition is 160.