LCM of 35, 12 and 70 is 420.The Least Common Divisor, or Least Common multiple or Lowest common multiple simply known as LCM is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 35, 12 and 70, 420 is the first(least or smallest) number that is common in the set of multiples of 35, 12 and 70. You can use the LCM with Examples to understand the LCM in detail.
What is LCM of 35, 12 and 70
The Least Common Multiple or Lowest Common Multiple of 35, 12 and 70 is 420.
How to Find LCM of 35, 12 and 70?
LCM of 35, 12 and 70 can be determined using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 35, 12 and 70 Using Prime Factorisation Method
In the Prime Factorisation method, the numbers can be expressed as the product of prime numbers. Here, 35, 12 and 70 can be expressed as;
35 = 5 × 7
12 = 2 × 2 × 3
70 = 2 × 5 × 7
LCM (35, 12, 70) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 35, 12 and 70 Using Division Method
In the Division Method, the given set of numbers 35, 12 and 70 are divided by prime divisors. These numbers are divided with the smallest number that divides all, until no further division is possible or only when prime numbers are left.
|
2 |
35 |
12 |
70 |
|
2 |
35 |
6 |
35 |
|
3 |
35 |
3 |
35 |
|
5 |
35 |
1 |
35 |
|
7 |
7 |
1 |
7 |
|
× |
1 |
1 |
1 |
LCM (35, 12, 70) = 2 × 2 × 3 × 5 × 7 = 420
LCM of 35, 12 and 70 Using Listing the Multiples
By listing all the multiples of given numbers, we can identify the first/smallest/least common multiple, which is the LCM. Below is the list of multiples for 35, 12 and 70
Multiples of 12
12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, 384, 396, 408, 420, 432, 444
Multiples of 35
35, 70, 105, 140, 175, 210, 245, 280, 315, 350, 385, 420, 455, 490
Multiples of 70
70, 140, 210, 280, 350, 420, 490, 560
LCM (35, 12, 70) = 2 × 2 × 3 × 5 × 7 = 420
Related Articles
Video Lesson on Applications of LCM
Solved Examples
What is the smallest number that is divisible by both 35, 12 and 70?
Answer: 420 is the smallest number that is divisible by both 35, 12 and 70.
What is the LCM for 2, 6, 10, 35, 12 and 70?
Answer: LCM for 2, 6, 10, 35, 12 and 70 is 420.
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