LCM of 40 and 90 is 360. Among all common multiples of 40 and 90, the LCM of 40 and 90 is the smallest number. (40, 80, 120, 160, 200, etc.) and (90, 180, 270, 360, etc.) are the first few multiples of 40 and 90. Prime factorization, division, and listing multiples are the three most frequent methods for calculating the LCM of 40 and 90. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers.
Also read: Least common multiple
What is LCM of 40 and 90?
The answer to this question is 360. The LCM of 40 and 90 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40 and 90, is the smallest positive integer 360 which is divisible by both 40 and 90 with no remainder.
How to Find LCM of 40 and 90?
LCM of 40 and 90 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40 and 90 Using Prime Factorisation Method
The prime factorisation of 40 and 90, respectively, is given by:
40 = (2 × 2 × 2 × 5) = 23 × 51 and
90 = (2 × 3 × 3 × 5) = 21 × 32 × 51
LCM (40, 90) = 360
LCM of 40 and 90 Using Division Method
We’ll divide the numbers (40, 90) by their prime factors to get the LCM of 40 and 90 using the division method (preferably common). The LCM of 40 and 90 is calculated by multiplying these divisors.
| 2 | 40 | 90 |
| 2 | 20 | 45 |
| 2 | 10 | 45 |
| 3 | 5 | 45 |
| 3 | 5 | 15 |
| 5 | 1 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (40, 90) = 360
LCM of 40 and 90 Using Listing the Multiples
To calculate the LCM of 40 and 90 by listing out the common multiples, list the multiples as shown below
| Multiples of 40 | Multiples of 90 |
| 40 | 90 |
| 80 | 180 |
| 120 | 270 |
| …. | 360 |
| 360 | 450 |
The smallest common multiple of 40 and 90 is 360.
Therefore LCM (40, 90) = 360
Related Articles
Video Lesson on Applications of LCM
LCM of 40 and 90 Solved Example
Find the smallest number that is divisible by 40 and 90 exactly.
Solution:
The smallest number that is divisible by 40 and 90 exactly is their LCM.
⇒ Multiples of 40 and 90:
Multiples of 40 = 40, 80, 120, 160, 200, 240, 280, 320, 360, . . . .
Multiples of 90 = 90, 180, 270, 360, 450, 540, 630, . . . .
Therefore, the LCM of 40 and 90 is 360.
Frequently Asked Questions on LCM of 40 and 90
What is the LCM of 40 and 90?
List the methods used to find the LCM of 40 and 90.
Which of the following is the LCM of 40 and 90? 15, 27, 40, 360
If the LCM of 90 and 40 is 360, Find its GCF.
Since the LCM of 90 and 40 = 360
⇒ 360 × GCF(90, 40) = 3600
Therefore, the GCF (greatest common factor) = 3600/360 = 10.
What is the Least Perfect Square Divisible by 40 and 90?
LCM of 40 and 90 = 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5] ⇒ Least perfect square divisible by each 40 and 90 = LCM(40, 90) × 2 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
Comments