LCM of 35 and 56 is 280. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The smallest number among all common multiples of 35 and 56 is the LCM of 35 and 56. (35, 70, 105, 140, 175, etc.) and (56, 112, 168, 224, 280, 336, 392, etc.) are the first few multiples of 35 and 56, respectively. Various approaches, such as prime factorization, division, and listing the multiples, can be used to quickly find the LCM.
Also read: Least common multiple
What is LCM of 35 and 56?
The answer to this question is 280. The LCM of 35 and 56 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 35 and 56, is the smallest positive integer 280 which is divisible by both 35 and 56 with no remainder.
How to Find LCM of 35 and 56?
LCM of 35 and 56 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 35 and 56 Using Prime Factorisation Method
The prime factorisation of 35 and 56, respectively, is given by:
35 = (5 × 7) = 51 × 71 and
56 = (2 × 2 × 2 × 7) = 23 × 71
LCM (35, 56) = 280
LCM of 35 and 56 Using Division Method
We’ll divide the numbers (35, 56) by their prime factors to get the LCM of 35 and 56 using the division method (preferably common). The LCM of 35 and 56 is calculated by multiplying these divisors.
| 2 | 35 | 56 |
| 2 | 35 | 28 |
| 2 | 35 | 14 |
| 5 | 35 | 7 |
| 7 | 7 | 7 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (35, 56) = 2280
LCM of 35 and 56 Using Listing the Multiples
To calculate the LCM of 35 and 56 by listing out the common multiples, list the multiples as shown below
| Multiples of 35 | Multiples of 56 |
| 35 | 56 |
| 70 | 112 |
| 105 | 168 |
| …… | 224 |
| 280 | 280 |
The smallest common multiple of 35 and 56 is 280.
Therefore LCM (35, 56) = 280
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LCM of 35 and 56 Solved Example
The GCD and LCM of two numbers are 7 and 280 respectively. If one number is 35, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 35 × p
⇒ p = (GCD × LCM)/35
⇒ p = (7 × 280)/35
⇒ p = 56
Therefore, the other number is 56.
Frequently Asked Questions on LCM of 35 and 56
What is the LCM of 35 and 56?
List the methods used to find the LCM of 35 and 56.
If the LCM of 56 and 35 is 280, Find its GCF.
Since the LCM of 56 and 35 = 280
⇒ 280 × GCF(56, 35) = 1960
Therefore, the greatest common factor (GCF) = 1960/280 = 7.
What is the Relation Between GCF and LCM of 35, 56?
How to Find the LCM of 35 and 56 by Prime Factorization?
⇒ LCM of 35, 56 = 23 × 51 × 71 = 280.
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