LCM of 12 and 35 is 420. In mathematics, the LCM of any two numbers is the value that is evenly divisible by both. Among all common multiples of 12 and 35, the LCM of 12 and 35 is the smallest. (12, 24, 36, 48, 60, 72, etc.) and (35, 70, 105, 140, 175, 210, etc.) respectively are the first few multiples of 12 and 35. The division technique, prime factorization, and listing multiples are the three most frequent ways for finding the LCM of 12 and 35.
What is LCM of 12 and 35?
The answer to this question is 420. The LCM of 12 and 35 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 12 and 35, is the smallest positive integer 420 which is divisible by both 12 and 35 with no remainder.
Also read: Least common multiple
How to Find LCM of 12 and 35?
LCM of 12 and 35 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 12 and 35 Using Prime Factorisation Method
The prime factorisation of 12 and 35, respectively, is given by:
12 = (2 × 2 × 3) = 22 × 31 and
35 = (5 × 7) = 51 × 71
LCM (12, 35) = 420
LCM of 12 and 35 Using Division Method
We’ll divide the numbers (12, 35) by their prime factors to get the LCM of 12 and 35 using the division method (preferably common). The LCM of 12 and 35 is calculated by multiplying these divisors.
| 2 | 12 | 35 |
| 2 | 6 | 35 |
| 3 | 3 | 35 |
| 5 | 1 | 35 |
| 7 | 1 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (12, 35) = 2 x 3 x 5 x 7 = 420
LCM of 12 and 35 Using Listing the Multiples
To calculate the LCM of 12 and 35 by listing out the common multiples, list the multiples as shown below
| Multiples of 12 | Multiples of 35 |
| 12 | 35 |
| 24 | 70 |
| 36 | 105 |
| 48 | 140 |
| 60 | 175 |
| 72 | 210 |
| 84 | 245 |
| . | 280 |
| . | 315 |
| . | 350 |
| . | 385 |
| 420 | 420 |
The smallest common multiple of 12 and 35 is 420.
LCM (12, 35) = 420
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LCM of 12 and 35 Solved Example
Question: The GCD and LCM of two numbers are 1 and 420 respectively. If one number is 12, find the other number.
Solution:
Let the other number be p.
GCD × LCM = 12 × p
p = (GCD × LCM)/12
p = (1 × 420)/12
p = 35
Therefore, the other number is 35.
Frequently Asked Questions on LCM of 12 and 35
What is the LCM of 12 and 35?
What is the Relation Between GCF and LCM of 12, 35?
If the LCM of 35 and 12 is 420, Find its GCF.
Since the LCM of 35 and 12 = 420
⇒ 420 × GCF(35, 12) = 420
Therefore, the greatest common factor = 420/420 = 1.
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