LCM of 60 and 80

LCM of 60 and 80 is the smallest number among all common multiples of 60 and 80. The first few multiples of 60 and 80 are (60, 120, 180, 240, 300, 360, 420, . . . ) and (80, 160, 240, 320, 400, 480, . . . ) respectively. There are 3 commonly used methods to find LCM of 60 and 80 - by prime factorization, by listing multiples, and by division method.

Answer: LCM of 60 and 80 is 240.

Explanation:

The LCM of two non-zero integers, x(60) and y(80), is the smallest positive integer m(240) that is divisible by both x(60) and y(80) without any remainder.

The methods to find the LCM of 60 and 80 are explained below.

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

LCM of 60 and 80 by Prime Factorization

Prime factorization of 60 and 80 is (2 × 2 × 3 × 5) = 2² × 3¹ × 5¹ and (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ respectively. LCM of 60 and 80 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5¹ = 240.
Hence, the LCM of 60 and 80 by prime factorization is 240.

LCM of 60 and 80 by Listing Multiples

To calculate the LCM of 60 and 80 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 60 (60, 120, 180, 240, 300, 360, 420, . . . ) and 80 (80, 160, 240, 320, 400, 480, . . . . )
• Step 2: The common multiples from the multiples of 60 and 80 are 240, 480, . . .
• Step 3: The smallest common multiple of 60 and 80 is 240.

∴ The least common multiple of 60 and 80 = 240.

LCM of 60 and 80 by Division Method

To calculate the LCM of 60 and 80 by the division method, we will divide the numbers(60, 80) by their prime factors (preferably common). The product of these divisors gives the LCM of 60 and 80.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 60 and 80. Write this prime number(2) on the left of the given numbers(60 and 80), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (60, 80) 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 60 and 80 is the product of all prime numbers on the left, i.e. LCM(60, 80) by division method = 2 × 2 × 2 × 2 × 3 × 5 = 240.

☛ Also Check:

• LCM of 5 and 10 - 10
• LCM of 2, 3 and 4 - 12
• LCM of 14 and 21 - 42
• LCM of 10 and 30 - 30
• LCM of 30 and 40 - 120
• LCM of 3, 5 and 8 - 120
• LCM of 20 and 50 - 100

FAQs on LCM of 60 and 80

What is the LCM of 60 and 80?

The LCM of 60 and 80 is 240. To find the LCM of 60 and 80, we need to find the multiples of 60 and 80 (multiples of 60 = 60, 120, 180, 240; multiples of 80 = 80, 160, 240, 320) and choose the smallest multiple that is exactly divisible by 60 and 80, i.e., 240.

If the LCM of 80 and 60 is 240, Find its GCF.

LCM(80, 60) × GCF(80, 60) = 80 × 60
Since the LCM of 80 and 60 = 240
⇒ 240 × GCF(80, 60) = 4800
Therefore, the greatest common factor = 4800/240 = 20.

What is the Least Perfect Square Divisible by 60 and 80?

The least number divisible by 60 and 80 = LCM(60, 80)
LCM of 60 and 80 = 2 × 2 × 2 × 2 × 3 × 5 [Incomplete pair(s): 3, 5]
⇒ Least perfect square divisible by each 60 and 80 = LCM(60, 80) × 3 × 5 = 3600 [Square root of 3600 = √3600 = ±60]
Therefore, 3600 is the required number.

What are the Methods to Find LCM of 60 and 80?

The commonly used methods to find the LCM of 60 and 80 are:

• Prime Factorization Method
• Division Method
• Listing Multiples

What is the Relation Between GCF and LCM of 60, 80?

The following equation can be used to express the relation between GCF and LCM of 60 and 80, i.e. GCF × LCM = 60 × 80.