LCM of 90 and 99 is 990. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. 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. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 90 and 99?
The answer to this question is 990. The LCM of 90 and 99 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 90 and 99, is the smallest positive integer 990 which is divisible by both 90 and 99 with no remainder.
How to Find LCM of 90 and 99?
LCM of 90 and 99 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 90 and 99 Using Prime Factorisation Method
The prime factorisation of 90 and 99, respectively, is given by:
90 = (2 × 3 × 3 × 5) = 21 × 32 × 51 and
99 = (3 × 3 × 11) = 32 × 111
LCM (90, 99) = 990
LCM of 90 and 99 Using Division Method
We’ll divide the numbers (90, 99) by their prime factors to get the LCM of 90 and 99 using the division method (preferably common). The LCM of 90 and 99 is calculated by multiplying these divisors.
| 3 | 90 | 99 |
| 3 | 30 | 33 |
| 2 | 10 | 11 |
| 5 | 5 | 11 |
| 11 | 1 | 11 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (90, 99) = 990
LCM of 90 and 99 Using Listing the Multiples
To calculate the LCM of 90 and 99 by listing out the common multiples, list the multiples as shown below
| Multiples of 90 | Multiples of 99 |
| 90 | 99 |
| 180 | 198 |
| 270 | 297 |
| ……. | ….. |
| 990 | 990 |
The smallest common multiple of 90 and 99 is 990.
Therefore LCM (90, 99) = 990
Related Articles
Video Lesson on Applications of LCM
LCM of 90 and 99 Solved Example
Question: The product of two numbers is 8910. If their GCD is 9, what is their LCM?
Solution:
Given: GCD = 9
product of numbers = 8910
LCM × GCD = product of numbers
LCM = Product/GCD = 8910/9
Therefore, the LCM is 990.
The probable combination for the given case is LCM(90, 99) = 990.
Frequently Asked Questions on LCM of 90 and 99
What is the LCM of 90 and 99?
List the methods used to find the LCM of 90 and 99.
If the LCM of 99 and 90 is 990, Find its GCF.
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?
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.
How to Find the LCM of 90 and 99 by Prime Factorization?
⇒ LCM of 90, 99 = 2 × 3 × 3 × 5 × 11 = 990.
Comments