LCM of 80 and 100

LCM of 80 and 100 is the smallest number among all common multiples of 80 and 100. The first few multiples of 80 and 100 are (80, 160, 240, 320, 400, 480, . . . ) and (100, 200, 300, 400, 500, 600, . . . ) respectively. There are 3 commonly used methods to find LCM of 80 and 100 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 80 and 100 is 400.

Explanation:

The LCM of two non-zero integers, x(80) and y(100), is the smallest positive integer m(400) that is divisible by both x(80) and y(100) without any remainder.

The methods to find the LCM of 80 and 100 are explained below.

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

LCM of 80 and 100 by Listing Multiples

To calculate the LCM of 80 and 100 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 80 (80, 160, 240, 320, 400, 480, . . . ) and 100 (100, 200, 300, 400, 500, 600, . . . . )
• Step 2: The common multiples from the multiples of 80 and 100 are 400, 800, . . .
• Step 3: The smallest common multiple of 80 and 100 is 400.

∴ The least common multiple of 80 and 100 = 400.

LCM of 80 and 100 by Division Method

To calculate the LCM of 80 and 100 by the division method, we will divide the numbers(80, 100) by their prime factors (preferably common). The product of these divisors gives the LCM of 80 and 100.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 80 and 100. Write this prime number(2) on the left of the given numbers(80 and 100), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (80, 100) 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 80 and 100 is the product of all prime numbers on the left, i.e. LCM(80, 100) by division method = 2 × 2 × 2 × 2 × 5 × 5 = 400.

LCM of 80 and 100 by Prime Factorization

Prime factorization of 80 and 100 is (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ and (2 × 2 × 5 × 5) = 2² × 5² respectively. LCM of 80 and 100 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 5² = 400.
Hence, the LCM of 80 and 100 by prime factorization is 400.

☛ Also Check:

• LCM of 15 and 27 - 135
• LCM of 14 and 20 - 140
• LCM of 12 and 60 - 60
• LCM of 2, 5 and 8 - 40
• LCM of 39 and 65 - 195
• LCM of 20, 30 and 60 - 60
• LCM of 16 and 64 - 64

FAQs on LCM of 80 and 100

What is the LCM of 80 and 100?

The LCM of 80 and 100 is 400. To find the least common multiple of 80 and 100, we need to find the multiples of 80 and 100 (multiples of 80 = 80, 160, 240, 320 . . . . 400; multiples of 100 = 100, 200, 300, 400) and choose the smallest multiple that is exactly divisible by 80 and 100, i.e., 400.

What is the Least Perfect Square Divisible by 80 and 100?

The least number divisible by 80 and 100 = LCM(80, 100)
LCM of 80 and 100 = 2 × 2 × 2 × 2 × 5 × 5 [No incomplete pair]
⇒ Least perfect square divisible by each 80 and 100 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.

How to Find the LCM of 80 and 100 by Prime Factorization?

To find the LCM of 80 and 100 using prime factorization, we will find the prime factors, (80 = 2 × 2 × 2 × 2 × 5) and (100 = 2 × 2 × 5 × 5). LCM of 80 and 100 is the product of prime factors raised to their respective highest exponent among the numbers 80 and 100.
⇒ LCM of 80, 100 = 2⁴ × 5² = 400.

What is the Relation Between GCF and LCM of 80, 100?

The following equation can be used to express the relation between GCF and LCM of 80 and 100, i.e. GCF × LCM = 80 × 100.

If the LCM of 100 and 80 is 400, Find its GCF.

LCM(100, 80) × GCF(100, 80) = 100 × 80
Since the LCM of 100 and 80 = 400
⇒ 400 × GCF(100, 80) = 8000
Therefore, the GCF (greatest common factor) = 8000/400 = 20.