LCM of 45 and 120 is 360. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Least common multiple of 45 and 120 is the smallest number we get among the common multiples. The first few multiples of 45 and 120 are (45, 90, 135, 180, 225, 270, . . . ) and (120, 240, 360, 480, 600, 720, . . . ) 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 45 and 120?
The answer to this question is 360. The LCM of 45 and 120 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 45 and 120, is the smallest positive integer 360 which is divisible by both 45 and 120 with no remainder.
How to Find LCM of 45 and 120?
LCM of 45 and 120 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 45 and 120 Using Prime Factorisation Method
The prime factorisation of 45 and 120, respectively, is given by:
45 = (3 × 3 × 5) = 32 × 51 and
120 = (2 × 2 × 2 × 3 × 5) = 23 × 31 × 51
LCM (45, 120) = 360
LCM of 45 and 120 Using Division Method
We’ll divide the numbers (45, 120) by their prime factors to get the LCM of 45 and 120 using the division method (preferably common). The LCM of 45 and 120 is calculated by multiplying these divisors.
| 2 | 45 | 120 |
| 2 | 45 | 60 |
| 2 | 45 | 30 |
| 3 | 45 | 15 |
| 3 | 15 | 5 |
| 5 | 5 | 5 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (45, 120) = 360
LCM of 45 and 120 Using Listing the Multiples
To calculate the LCM of 45 and 120 by listing out the common multiples, list the multiples as shown below.
| Multiples of 45 | Multiples of 120 |
| 45 | 120 |
| 90 | 240 |
| 135 | 360 |
| 180 | 480 |
| ……. | 600 |
| 360 | 720 |
The smallest common multiple of 45 and 120 is 360.
Therefore LCM (45, 120) = 360
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LCM of 45 and 120 Solved Example
Question: The GCD and LCM of two numbers are 15 and 360 respectively. If one number is 120, find the other number.
Solution:
Let the other number be y.
∵ GCD × LCM = 120 × y
⇒ y = (GCD × LCM)/120
⇒ y = (15 × 360)/120
⇒ y = 45
Therefore, the other number is 45.
Frequently Asked Questions on LCM of 45 and 120
What is the LCM of 45 and 120?
List the methods used to find the LCM of 45 and 120.
If the LCM of 120 and 45 is 360, Find its GCF.
Since the LCM of 120 and 45 = 360
⇒ 360 × GCF(120, 45) = 5400
Therefore, the greatest common factor (GCF) = 5400/360 = 15.
Which of the following is the LCM of 45 and 120? 15, 32, 50, 360
What is the Least Perfect Square Divisible by 45 and 120?
LCM of 45 and 120 = 2 × 2 × 2 × 3 × 3 × 5 [Incomplete pair(s): 2, 5] ⇒ Least perfect square divisible by each 45 and 120 = LCM(45, 120) × 2 × 5 = 3600 [Square root of 3600 = √3600 = ±60] Therefore, 3600 is the required number.
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