LCM of 35 and 50 is 350. The smallest number among all common multiples of 35 and 50 is the LCM of 35 and 50. (35, 70, 105, 140, 175, 210, etc.) and (50, 100, 150, 200, 250, 300, 350, etc.) are the first few multiples of 35 and 50, respectively. To find the LCM of 35 and 50, there are three typical methods: listing multiples, division method, and prime factorization. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values.
Also read: Least common multiple
What is LCM of 35 and 50?
The answer to this question is 350. The LCM of 35 and 50 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 35 and 50, is the smallest positive integer 350 which is divisible by both 35 and 50 with no remainder.
How to Find LCM of 35 and 50?
LCM of 35 and 50 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 35 and 50 Using Prime Factorisation Method
The prime factorisation of 35 and 50, respectively, is given by:
35 = (5 × 7) = 51 × 71 and
50 = (2 × 5 × 5) = 21 × 52
LCM (35, 50) = 350
LCM of 35 and 50 Using Division Method
We’ll divide the numbers (35, 50) by their prime factors to get the LCM of 35 and 50 using the division method (preferably common). The LCM of 35 and 50 is calculated by multiplying these divisors.
| 2 | 35 | 50 |
| 5 | 35 | 25 |
| 5 | 7 | 5 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (35, 50) = 350
LCM of 35 and 50 Using Listing the Multiples
To calculate the LCM of 35 and 50 by listing out the common multiples, list the multiples as shown below
| Multiples of 35 | Multiples of 50 |
| 35 | 50 |
| 70 | 100 |
| 105 | 150 |
| ….. | ….. |
| 350 | 350 |
The smallest common multiple of 35 and 50 is 350.
Therefore LCM (35, 50) = 350
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LCM of 35 and 50 Solved Example
Question: The product of two numbers is 1750. If their GCD is 5, what is their LCM?
Solution:
Given: GCD = 5
Product of numbers = 1750
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 1750/5
Therefore, the LCM is 350.
The probable combination for the given case is LCM(35, 50) = 350.
Frequently Asked Questions on LCM of 35 and 50
What is the LCM of 35 and 50?
List the methods used to find the LCM of 35 and 50.
What is the Relation Between GCF and LCM of 35, 50?
What is the Least Perfect Square Divisible by 35 and 50?
LCM of 35 and 50 = 2 × 5 × 5 × 7 [Incomplete pair(s): 2, 7] ⇒ Least perfect square divisible by each 35 and 50 = LCM(35, 50) × 2 × 7 = 4900 [Square root of 4900 = √4900 = ±70] Therefore, 4900 is the required number..
If the LCM of 50 and 35 is 350, Find its GCF.
Since the LCM of 50 and 35 = 350
⇒ 350 × GCF(50, 35) = 1750
Therefore, the GCF (greatest common factor) = 1750/350 = 5.
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