LCM of 12 and 84

LCM of 12 and 84 is the smallest number among all common multiples of 12 and 84. The first few multiples of 12 and 84 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (84, 168, 252, 336, 420, 504, . . . ) respectively. There are 3 commonly used methods to find LCM of 12 and 84 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 12 and 84 is 84.

Explanation:

The LCM of two non-zero integers, x(12) and y(84), is the smallest positive integer m(84) that is divisible by both x(12) and y(84) without any remainder.

The methods to find the LCM of 12 and 84 are explained below.

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

LCM of 12 and 84 by Prime Factorization

Prime factorization of 12 and 84 is (2 × 2 × 3) = 2² × 3¹ and (2 × 2 × 3 × 7) = 2² × 3¹ × 7¹ respectively. LCM of 12 and 84 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2² × 3¹ × 7¹ = 84.
Hence, the LCM of 12 and 84 by prime factorization is 84.

LCM of 12 and 84 by Listing Multiples

To calculate the LCM of 12 and 84 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 12 (12, 24, 36, 48, 60, 72, 84, . . . ) and 84 (84, 168, 252, 336, 420, 504, . . . . )
• Step 2: The common multiples from the multiples of 12 and 84 are 84, 168, . . .
• Step 3: The smallest common multiple of 12 and 84 is 84.

∴ The least common multiple of 12 and 84 = 84.

LCM of 12 and 84 by Division Method

To calculate the LCM of 12 and 84 by the division method, we will divide the numbers(12, 84) by their prime factors (preferably common). The product of these divisors gives the LCM of 12 and 84.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 12 and 84. Write this prime number(2) on the left of the given numbers(12 and 84), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (12, 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 12 and 84 is the product of all prime numbers on the left, i.e. LCM(12, 84) by division method = 2 × 2 × 3 × 7 = 84.

☛ Also Check:

• LCM of 6, 10 and 12 - 60
• LCM of 5, 9 and 15 - 45
• LCM of 5, 8 and 12 - 120
• LCM of 5, 8 and 15 - 120
• LCM of 5, 7 and 9 - 315
• LCM of 5, 7 and 10 - 70
• LCM of 5, 6 and 8 - 120

FAQs on LCM of 12 and 84

What is the LCM of 12 and 84?

The LCM of 12 and 84 is 84. To find the least common multiple (LCM) of 12 and 84, we need to find the multiples of 12 and 84 (multiples of 12 = 12, 24, 36, 48 . . . . 84; multiples of 84 = 84, 168, 252, 336) and choose the smallest multiple that is exactly divisible by 12 and 84, i.e., 84.

How to Find the LCM of 12 and 84 by Prime Factorization?

To find the LCM of 12 and 84 using prime factorization, we will find the prime factors, (12 = 2 × 2 × 3) and (84 = 2 × 2 × 3 × 7). LCM of 12 and 84 is the product of prime factors raised to their respective highest exponent among the numbers 12 and 84.
⇒ LCM of 12, 84 = 2² × 3¹ × 7¹ = 84.

If the LCM of 84 and 12 is 84, Find its GCF.

LCM(84, 12) × GCF(84, 12) = 84 × 12
Since the LCM of 84 and 12 = 84
⇒ 84 × GCF(84, 12) = 1008
Therefore, the GCF = 1008/84 = 12.

Which of the following is the LCM of 12 and 84? 27, 36, 84, 32

The value of LCM of 12, 84 is the smallest common multiple of 12 and 84. The number satisfying the given condition is 84.

What is the Least Perfect Square Divisible by 12 and 84?

The least number divisible by 12 and 84 = LCM(12, 84)
LCM of 12 and 84 = 2 × 2 × 3 × 7 [Incomplete pair(s): 3, 7]
⇒ Least perfect square divisible by each 12 and 84 = LCM(12, 84) × 3 × 7 = 1764 [Square root of 1764 = √1764 = ±42]
Therefore, 1764 is the required number.