LCM of 72 and 24

LCM of 72 and 24 is the smallest number among all common multiples of 72 and 24. The first few multiples of 72 and 24 are (72, 144, 216, 288, . . . ) and (24, 48, 72, 96, 120, . . . ) respectively. There are 3 commonly used methods to find LCM of 72 and 24 - by division method, by prime factorization, and by listing multiples.

Answer: LCM of 72 and 24 is 72.

Explanation:

The LCM of two non-zero integers, x(72) and y(24), is the smallest positive integer m(72) that is divisible by both x(72) and y(24) without any remainder.

Let's look at the different methods for finding the LCM of 72 and 24.

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

LCM of 72 and 24 by Listing Multiples

To calculate the LCM of 72 and 24 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 72 (72, 144, 216, 288, . . . ) and 24 (24, 48, 72, 96, 120, . . . . )
• Step 2: The common multiples from the multiples of 72 and 24 are 72, 144, . . .
• Step 3: The smallest common multiple of 72 and 24 is 72.

∴ The least common multiple of 72 and 24 = 72.

LCM of 72 and 24 by Prime Factorization

Prime factorization of 72 and 24 is (2 × 2 × 2 × 3 × 3) = 2³ × 3² and (2 × 2 × 2 × 3) = 2³ × 3¹ respectively. LCM of 72 and 24 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² = 72.
Hence, the LCM of 72 and 24 by prime factorization is 72.

LCM of 72 and 24 by Division Method

To calculate the LCM of 72 and 24 by the division method, we will divide the numbers(72, 24) by their prime factors (preferably common). The product of these divisors gives the LCM of 72 and 24.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 72 and 24. Write this prime number(2) on the left of the given numbers(72 and 24), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (72, 24) 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 72 and 24 is the product of all prime numbers on the left, i.e. LCM(72, 24) by division method = 2 × 2 × 2 × 3 × 3 = 72.

☛ Also Check:

• LCM of 30 and 36 - 180
• LCM of 8, 12 and 15 - 120
• LCM of 40 and 50 - 200
• LCM of 2, 4 and 7 - 28
• LCM of 6, 12 and 18 - 36
• LCM of 45, 60 and 75 - 900
• LCM of 15 and 18 - 90

FAQs on LCM of 72 and 24

What is the LCM of 72 and 24?

The LCM of 72 and 24 is 72. To find the least common multiple (LCM) of 72 and 24, we need to find the multiples of 72 and 24 (multiples of 72 = 72, 144, 216, 288; multiples of 24 = 24, 48, 72, 96) and choose the smallest multiple that is exactly divisible by 72 and 24, i.e., 72.

What is the Least Perfect Square Divisible by 72 and 24?

The least number divisible by 72 and 24 = LCM(72, 24)
LCM of 72 and 24 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 72 and 24 = LCM(72, 24) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

If the LCM of 24 and 72 is 72, Find its GCF.

LCM(24, 72) × GCF(24, 72) = 24 × 72
Since the LCM of 24 and 72 = 72
⇒ 72 × GCF(24, 72) = 1728
Therefore, the greatest common factor = 1728/72 = 24.

What is the Relation Between GCF and LCM of 72, 24?

The following equation can be used to express the relation between GCF and LCM of 72 and 24, i.e. GCF × LCM = 72 × 24.

What are the Methods to Find LCM of 72 and 24?

The commonly used methods to find the LCM of 72 and 24 are:

• Division Method
• Listing Multiples
• Prime Factorization Method