LCM of 80 and 84

LCM of 80 and 84 is the smallest number among all common multiples of 80 and 84. The first few multiples of 80 and 84 are (80, 160, 240, 320, . . . ) and (84, 168, 252, 336, 420, 504, . . . ) respectively. There are 3 commonly used methods to find LCM of 80 and 84 - by prime factorization, by division method, and by listing multiples.

Answer: LCM of 80 and 84 is 1680.

Explanation:

The LCM of two non-zero integers, x(80) and y(84), is the smallest positive integer m(1680) that is divisible by both x(80) and y(84) without any remainder.

Let's look at the different methods for finding the LCM of 80 and 84.

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

LCM of 80 and 84 by Listing Multiples

To calculate the LCM of 80 and 84 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, . . . ) and 84 (84, 168, 252, 336, 420, 504, . . . . )
• Step 2: The common multiples from the multiples of 80 and 84 are 1680, 3360, . . .
• Step 3: The smallest common multiple of 80 and 84 is 1680.

∴ The least common multiple of 80 and 84 = 1680.

LCM of 80 and 84 by Division Method

To calculate the LCM of 80 and 84 by the division method, we will divide the numbers(80, 84) by their prime factors (preferably common). The product of these divisors gives the LCM of 80 and 84.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 80 and 84. Write this prime number(2) on the left of the given numbers(80 and 84), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (80, 84) 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 84 is the product of all prime numbers on the left, i.e. LCM(80, 84) by division method = 2 × 2 × 2 × 2 × 3 × 5 × 7 = 1680.

LCM of 80 and 84 by Prime Factorization

Prime factorization of 80 and 84 is (2 × 2 × 2 × 2 × 5) = 2⁴ × 5¹ and (2 × 2 × 3 × 7) = 2² × 3¹ × 7¹ respectively. LCM of 80 and 84 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2⁴ × 3¹ × 5¹ × 7¹ = 1680.
Hence, the LCM of 80 and 84 by prime factorization is 1680.

☛ Also Check:

• LCM of 5, 10, 15 and 30 - 30
• LCM of 18 and 40 - 360
• LCM of 5, 15 and 20 - 60
• LCM of 40 and 50 - 200
• LCM of 8 and 28 - 56
• LCM of 28 and 32 - 224
• LCM of 42 and 63 - 126

FAQs on LCM of 80 and 84

What is the LCM of 80 and 84?

The LCM of 80 and 84 is 1680. To find the LCM (least common multiple) of 80 and 84, we need to find the multiples of 80 and 84 (multiples of 80 = 80, 160, 240, 320 . . . . 1680; multiples of 84 = 84, 168, 252, 336 . . . . 1680) and choose the smallest multiple that is exactly divisible by 80 and 84, i.e., 1680.

What is the Least Perfect Square Divisible by 80 and 84?

The least number divisible by 80 and 84 = LCM(80, 84)
LCM of 80 and 84 = 2 × 2 × 2 × 2 × 3 × 5 × 7 [Incomplete pair(s): 3, 5, 7]
⇒ Least perfect square divisible by each 80 and 84 = LCM(80, 84) × 3 × 5 × 7 = 176400 [Square root of 176400 = √176400 = ±420]
Therefore, 176400 is the required number.

If the LCM of 84 and 80 is 1680, Find its GCF.

LCM(84, 80) × GCF(84, 80) = 84 × 80
Since the LCM of 84 and 80 = 1680
⇒ 1680 × GCF(84, 80) = 6720
Therefore, the GCF (greatest common factor) = 6720/1680 = 4.

Which of the following is the LCM of 80 and 84? 28, 45, 15, 1680

The value of LCM of 80, 84 is the smallest common multiple of 80 and 84. The number satisfying the given condition is 1680.

What are the Methods to Find LCM of 80 and 84?

The commonly used methods to find the LCM of 80 and 84 are:

• Division Method
• Listing Multiples
• Prime Factorization Method