LCM of 30 and 35 is 210. 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. The smallest number among all common multiples of 30 and 35 is the LCM of 30 and 35. (30, 60, 90, 120, 150, 180, etc.) and (35, 70, 105, 140, etc.) are the first few multiples of 30 and 35, respectively.
Also read: Least common multiple
What is LCM of 30 and 35?
The answer to this question is 210. The LCM of 30 and 35 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 30 and 35, is the smallest positive integer 210 which is divisible by both 30 and 35 with no remainder.
How to Find LCM of 30 and 35?
LCM of 30 and 35 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 30 and 35 Using Prime Factorisation Method
The prime factorisation of 30 and 35, respectively, is given by:
30 = (2 × 3 × 5) = 21 × 31 × 51 and
35 = (5 × 7) = 51 × 71
LCM (30, 35) = 210
LCM of 30 and 35 Using Division Method
We’ll divide the numbers (30, 35) by their prime factors to get the LCM of 30 and 35 using the division method (preferably common). The LCM of 30 and 35 is calculated by multiplying these divisors.
| 2 | 30 | 35 |
| 3 | 15 | 35 |
| 5 | 5 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (30, 35) = 210
LCM of 30 and 35 Using Listing the Multiples
To calculate the LCM of 30 and 35 by listing out the common multiples, list the multiples as shown below
| Multiples of 30 | Multiples of 35 |
| 30 | 35 |
| 60 | 70 |
| 90 | 105 |
| 120 | 140 |
| 150 | 175 |
| 180 | 210 |
| 210 | 245 |
The smallest common multiple of 30 and 35 is 210.
Therefore LCM (30, 35) = 210
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Video Lesson on Applications of LCM
LCM of 30 and 35 Solved Example
Question: Verify the relationship between GCF and LCM of 30 and 35.
Solution:
The relation between GCF and LCM of 30 and 35 is given as,
LCM(30, 35) × GCF(30, 35) = Product of 30, 35
Prime factorization of 30 and 35 is given as, 30 = (2 × 3 × 5) = 2 × 3 × 5 and 35 = (5 × 7) = 51 × 71
LCM(30, 35) = 210
GCF(30, 35) = 5
LHS = LCM(30, 35) × GCF(30, 35) = 210 × 5 = 1050
RHS = Product of 30, 35 = 30 × 35 = 1050
⇒ LHS = RHS = 1050
Hence, verified.
Frequently Asked Questions on LCM of 30 and 35
What is the LCM of 30 and 35?
List the methods used to find the LCM of 30 and 35.
If the LCM of 35 and 30 is 210, Find its GCF.
Since the LCM of 35 and 30 = 210
⇒ 210 × GCF(35, 30) = 1050
Therefore, the greatest common factor = 1050/210 = 5.
Which of the following is the LCM of 30 and 35? 210, 32, 15, 11
What is the Least Perfect Square Divisible by 30 and 35?
LCM of 30 and 35 = 2 × 3 × 5 × 7 [Incomplete pair(s): 2, 3, 5, 7] ⇒ Least perfect square divisible by each 30 and 35 = LCM(30, 35) × 2 × 3 × 5 × 7 = 44100 [Square root of 44100 = √44100 = ±210] Therefore, 44100 is the required number.
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