LCM of 9 and 72

LCM of 9 and 72 is the smallest number among all common multiples of 9 and 72. The first few multiples of 9 and 72 are (9, 18, 27, 36, 45, 54, . . . ) and (72, 144, 216, 288, 360, . . . ) respectively. There are 3 commonly used methods to find LCM of 9 and 72 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 9 and 72 is 72.

Explanation:

The LCM of two non-zero integers, x(9) and y(72), is the smallest positive integer m(72) that is divisible by both x(9) and y(72) without any remainder.

Let's look at the different methods for finding the LCM of 9 and 72.

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

LCM of 9 and 72 by Listing Multiples

To calculate the LCM of 9 and 72 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 9 (9, 18, 27, 36, 45, 54, . . . ) and 72 (72, 144, 216, 288, 360, . . . . )
• Step 2: The common multiples from the multiples of 9 and 72 are 72, 144, . . .
• Step 3: The smallest common multiple of 9 and 72 is 72.

∴ The least common multiple of 9 and 72 = 72.

LCM of 9 and 72 by Division Method

To calculate the LCM of 9 and 72 by the division method, we will divide the numbers(9, 72) by their prime factors (preferably common). The product of these divisors gives the LCM of 9 and 72.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 9 and 72. Write this prime number(2) on the left of the given numbers(9 and 72), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (9, 72) 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 9 and 72 is the product of all prime numbers on the left, i.e. LCM(9, 72) by division method = 2 × 2 × 2 × 3 × 3 = 72.

LCM of 9 and 72 by Prime Factorization

Prime factorization of 9 and 72 is (3 × 3) = 3² and (2 × 2 × 2 × 3 × 3) = 2³ × 3² respectively. LCM of 9 and 72 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² = 72.
Hence, the LCM of 9 and 72 by prime factorization is 72.

☛ Also Check:

• LCM of 8, 9 and 12 - 72
• LCM of 11 and 121 - 121
• LCM of 3, 6 and 9 - 18
• LCM of 200 and 300 - 600
• LCM of 2 and 11 - 22
• LCM of 5 and 14 - 70
• LCM of 36 and 90 - 180

FAQs on LCM of 9 and 72

What is the LCM of 9 and 72?

The LCM of 9 and 72 is 72. To find the least common multiple (LCM) of 9 and 72, we need to find the multiples of 9 and 72 (multiples of 9 = 9, 18, 27, 36 . . . . 72; multiples of 72 = 72, 144, 216, 288) and choose the smallest multiple that is exactly divisible by 9 and 72, i.e., 72.

What is the Relation Between GCF and LCM of 9, 72?

The following equation can be used to express the relation between GCF and LCM of 9 and 72, i.e. GCF × LCM = 9 × 72.

What are the Methods to Find LCM of 9 and 72?

The commonly used methods to find the LCM of 9 and 72 are:

• Prime Factorization Method
• Listing Multiples
• Division Method

What is the Least Perfect Square Divisible by 9 and 72?

The least number divisible by 9 and 72 = LCM(9, 72)
LCM of 9 and 72 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 9 and 72 = LCM(9, 72) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

If the LCM of 72 and 9 is 72, Find its GCF.

LCM(72, 9) × GCF(72, 9) = 72 × 9
Since the LCM of 72 and 9 = 72
⇒ 72 × GCF(72, 9) = 648
Therefore, the greatest common factor (GCF) = 648/72 = 9.