LCM of 90 and 99

LCM of 90 and 99 is the smallest number among all common multiples of 90 and 99. The first few multiples of 90 and 99 are (90, 180, 270, 360, 450, 540, 630, . . . ) and (99, 198, 297, 396, . . . ) respectively. There are 3 commonly used methods to find LCM of 90 and 99 - by listing multiples, by division method, and by prime factorization.

Answer: LCM of 90 and 99 is 990.

Explanation:

The LCM of two non-zero integers, x(90) and y(99), is the smallest positive integer m(990) that is divisible by both x(90) and y(99) without any remainder.

The methods to find the LCM of 90 and 99 are explained below.

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

LCM of 90 and 99 by Prime Factorization

Prime factorization of 90 and 99 is (2 × 3 × 3 × 5) = 2¹ × 3² × 5¹ and (3 × 3 × 11) = 3² × 11¹ respectively. LCM of 90 and 99 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2¹ × 3² × 5¹ × 11¹ = 990.
Hence, the LCM of 90 and 99 by prime factorization is 990.

LCM of 90 and 99 by Division Method

To calculate the LCM of 90 and 99 by the division method, we will divide the numbers(90, 99) by their prime factors (preferably common). The product of these divisors gives the LCM of 90 and 99.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 90 and 99. Write this prime number(2) on the left of the given numbers(90 and 99), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (90, 99) 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 90 and 99 is the product of all prime numbers on the left, i.e. LCM(90, 99) by division method = 2 × 3 × 3 × 5 × 11 = 990.

LCM of 90 and 99 by Listing Multiples

To calculate the LCM of 90 and 99 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 90 (90, 180, 270, 360, 450, 540, 630, . . . ) and 99 (99, 198, 297, 396, . . . . )
• Step 2: The common multiples from the multiples of 90 and 99 are 990, 1980, . . .
• Step 3: The smallest common multiple of 90 and 99 is 990.

∴ The least common multiple of 90 and 99 = 990.

☛ Also Check:

• LCM of 7 and 10 - 70
• LCM of 24, 36 and 48 - 144
• LCM of 5 and 13 - 65
• LCM of 48 and 120 - 240
• LCM of 3, 5 and 11 - 165
• LCM of 10 and 40 - 40
• LCM of 20 and 60 - 60

FAQs on LCM of 90 and 99

What is the LCM of 90 and 99?

The LCM of 90 and 99 is 990. To find the least common multiple (LCM) of 90 and 99, we need to find the multiples of 90 and 99 (multiples of 90 = 90, 180, 270, 360 . . . . 990; multiples of 99 = 99, 198, 297, 396 . . . . 990) and choose the smallest multiple that is exactly divisible by 90 and 99, i.e., 990.

How to Find the LCM of 90 and 99 by Prime Factorization?

To find the LCM of 90 and 99 using prime factorization, we will find the prime factors, (90 = 2 × 3 × 3 × 5) and (99 = 3 × 3 × 11). LCM of 90 and 99 is the product of prime factors raised to their respective highest exponent among the numbers 90 and 99.
⇒ LCM of 90, 99 = 2¹ × 3² × 5¹ × 11¹ = 990.

What are the Methods to Find LCM of 90 and 99?

The commonly used methods to find the LCM of 90 and 99 are:

• Listing Multiples
• Division Method
• Prime Factorization Method

If the LCM of 99 and 90 is 990, Find its GCF.

LCM(99, 90) × GCF(99, 90) = 99 × 90
Since the LCM of 99 and 90 = 990
⇒ 990 × GCF(99, 90) = 8910
Therefore, the GCF = 8910/990 = 9.

What is the Least Perfect Square Divisible by 90 and 99?

The least number divisible by 90 and 99 = LCM(90, 99)
LCM of 90 and 99 = 2 × 3 × 3 × 5 × 11 [Incomplete pair(s): 2, 5, 11]
⇒ Least perfect square divisible by each 90 and 99 = LCM(90, 99) × 2 × 5 × 11 = 108900 [Square root of 108900 = √108900 = ±330]
Therefore, 108900 is the required number.