LCM of 24 and 84

LCM of 24 and 84 is the smallest number among all common multiples of 24 and 84. The first few multiples of 24 and 84 are (24, 48, 72, 96, 120, . . . ) and (84, 168, 252, 336, 420, . . . ) respectively. There are 3 commonly used methods to find LCM of 24 and 84 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 24 and 84 is 168.

Explanation:

The LCM of two non-zero integers, x(24) and y(84), is the smallest positive integer m(168) that is divisible by both x(24) and y(84) without any remainder.

The methods to find the LCM of 24 and 84 are explained below.

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

LCM of 24 and 84 by Division Method

To calculate the LCM of 24 and 84 by the division method, we will divide the numbers(24, 84) by their prime factors (preferably common). The product of these divisors gives the LCM of 24 and 84.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 24 and 84. Write this prime number(2) on the left of the given numbers(24 and 84), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (24, 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 24 and 84 is the product of all prime numbers on the left, i.e. LCM(24, 84) by division method = 2 × 2 × 2 × 3 × 7 = 168.

LCM of 24 and 84 by Prime Factorization

Prime factorization of 24 and 84 is (2 × 2 × 2 × 3) = 2³ × 3¹ and (2 × 2 × 3 × 7) = 2² × 3¹ × 7¹ respectively. LCM of 24 and 84 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3¹ × 7¹ = 168.
Hence, the LCM of 24 and 84 by prime factorization is 168.

LCM of 24 and 84 by Listing Multiples

To calculate the LCM of 24 and 84 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 24 (24, 48, 72, 96, 120, . . . ) and 84 (84, 168, 252, 336, 420, . . . . )
• Step 2: The common multiples from the multiples of 24 and 84 are 168, 336, . . .
• Step 3: The smallest common multiple of 24 and 84 is 168.

∴ The least common multiple of 24 and 84 = 168.

☛ Also Check:

• LCM of 12, 16 and 18 - 144
• LCM of 75 and 80 - 1200
• LCM of 3 and 14 - 42
• LCM of 45 and 54 - 270
• LCM of 15, 25, 40 and 75 - 600
• LCM of 30 and 48 - 240
• LCM of 42 and 72 - 504

FAQs on LCM of 24 and 84

What is the LCM of 24 and 84?

The LCM of 24 and 84 is 168. To find the LCM of 24 and 84, we need to find the multiples of 24 and 84 (multiples of 24 = 24, 48, 72, 96 . . . . 168; multiples of 84 = 84, 168, 252, 336) and choose the smallest multiple that is exactly divisible by 24 and 84, i.e., 168.

What is the Relation Between GCF and LCM of 24, 84?

The following equation can be used to express the relation between GCF and LCM of 24 and 84, i.e. GCF × LCM = 24 × 84.

What are the Methods to Find LCM of 24 and 84?

The commonly used methods to find the LCM of 24 and 84 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

If the LCM of 84 and 24 is 168, Find its GCF.

LCM(84, 24) × GCF(84, 24) = 84 × 24
Since the LCM of 84 and 24 = 168
⇒ 168 × GCF(84, 24) = 2016
Therefore, the greatest common factor (GCF) = 2016/168 = 12.

What is the Least Perfect Square Divisible by 24 and 84?

The least number divisible by 24 and 84 = LCM(24, 84)
LCM of 24 and 84 = 2 × 2 × 2 × 3 × 7 [Incomplete pair(s): 2, 3, 7]
⇒ Least perfect square divisible by each 24 and 84 = LCM(24, 84) × 2 × 3 × 7 = 7056 [Square root of 7056 = √7056 = ±84]
Therefore, 7056 is the required number.