LCM of 20 and 32 is 160. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. Least common multiple of 20 and 32 is the smallest number among all common multiples of 20 and 32. The first few multiples of 20 and 32 are (20, 40, 60, 80, 100, 120, 140, . . . ) and (32, 64, 96, 128, 160, . . . ) respectively.
Also read: Least common multiple
What is LCM of 20 and 32?
The answer to this question is 160. The LCM of 20 and 32 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 20 and 32, is the smallest positive integer 160 which is divisible by both 20 and 32 with no remainder.
How to Find LCM of 20 and 32?
LCM of 20 and 32 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 20 and 32 Using Prime Factorisation Method
The prime factorisation of 20 and 32, respectively, is given by:
20 = (2 × 2 × 5) = 22 × 51 and
32 = (2 × 2 × 2 × 2 × 2) = 25
LCM (20, 32) = 160
LCM of 20 and 32 Using Division Method
We’ll divide the numbers (20, 32) by their prime factors to get the LCM of 20 and 32 using the division method (preferably common). The LCM of 20 and 32 is calculated by multiplying these divisors.
| 2 | 20 | 32 |
| 2 | 10 | 16 |
| 2 | 5 | 8 |
| 2 | 5 | 4 |
| 2 | 5 | 2 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (20, 32) = 160
LCM of 20 and 32 Using Listing the Multiples
To calculate the LCM of 20 and 32 by listing out the common multiples, list the multiples as shown below
| Multiples of 20 | Multiples of 32 |
| 20 | 32 |
| 40 | 64 |
| 60 | 96 |
| …… | 128 |
| 160 | 160 |
The smallest common multiple of 20 and 32 is 160.
Therefore LCM (20, 32) = 160
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LCM of 20 and 32 Solved Example
Question: The GCD and LCM of two numbers are 4 and 160 respectively. If one number is 32, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 32 × p
⇒ p = (GCD × LCM)/32
⇒ p = (4 × 160)/32
⇒ p = 20
Therefore, the other number is 20.
Frequently Asked Questions on LCM of 20 and 32
What is the LCM of 20 and 32?
List the methods used to find the LCM of 20 and 32.
If the LCM of 32 and 20 is 160, Find its GCF.
Since the LCM of 32 and 20 = 160
⇒ 160 × GCF(32, 20) = 640
Therefore, the GCF = 640/160 = 4.
What is the Least Perfect Square Divisible by 20 and 32?
LCM of 20 and 32 = 2 × 2 × 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5] ⇒ Least perfect square divisible by each 20 and 32 = LCM(20, 32) × 2 × 5 = 1600 [Square root of 1600 = √1600 = ±40] Therefore, 1600 is the required number.
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