LCM of 10 and 14 is 70. 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 10 and 14 is the LCM of 10 and 14. (10, 20, 30, 40, 50, 60, etc.) and (14, 28, 42, 56, etc.) are the first few multiples of 10 and 14, respectively. To find the LCM of 10 and 14, there are three typical methods: division, prime factorization, and listing multiples.
Also read: Least common multiple
What is LCM of 10 and 14?
The answer to this question is 70. The LCM of 10 and 14 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 10 and 14, is the smallest positive integer 70 which is divisible by both 10 and 14 with no remainder.
How to Find LCM of 10 and 14?
LCM of 10 and 14 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 10 and 14 Using Prime Factorisation Method
The prime factorisation of 10 and 14, respectively, is given by:
10 = (2 × 5) = 21 × 51 and
14 = (2 × 7) = 21 × 71
LCM (10, 14) = 70
LCM of 10 and 14 Using Division Method
We’ll divide the numbers (10, 14) by their prime factors to get the LCM of 10 and 14 using the division method (preferably common). The LCM of 10 and 14 is calculated by multiplying these divisors.
| 2 | 10 | 14 |
| 5 | 5 | 7 |
| 7 | 1 | 7 |
| 1 | 1 |
No further division can be done.
Hence, LCM (10, 14) = 70
LCM of 10 and 14 Using Listing the Multiples
To calculate the LCM of 10 and 14 by listing out the common multiples, list the multiples as shown below
| Multiples of 10 | Multiples of 14 |
| 10 | 14 |
| 20 | 28 |
| 30 | 42 |
| 40 | 56 |
| 50 | 70 |
| 60 | |
| 70 |
The smallest common multiple of 10 and 14 is 70.
Therefore LCM (10, 14) = 70
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LCM of 10 and 14 Solved Examples
Find the smallest number that is divisible by 10 and 14 exactly.
Solution:
The smallest number that is divisible by 10 and 14 exactly is their LCM.
⇒ Multiples of 10 and 14:
Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, . . . .
Multiples of 14 = 14, 28, 42, 56, 70, . . . .
Therefore, the LCM of 10 and 14 is 70.
Frequently Asked Questions on LCM of 10 and 14
What is the LCM of 10 and 14?
Which of the following is the LCM of 10 and 14? 2, 45, 70, 27
If the LCM of 14 and 10 is 70, Find its GCF.
Since the LCM of 14 and 10 = 70
⇒ 70 × GCF(14, 10) = 140
Therefore, the greatest common factor (GCF) = 140/70 = 2.
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