LCM of 140 and 168 is 840. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. Least common multiple of 140 and 168 is the smallest number we get among the common multiples. (24, 48, 72, 96, ….) and (36, 72, 108, 144,….) are the first few multiples of 140 and 168. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 140 and 168?
The answer to this question is 840. The LCM of 140 and 168 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 140 and 168, is the smallest positive integer 840 which is divisible by both 140 and 168 with no remainder.
How to Find LCM of 140 and 168?
LCM of 140 and 168 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 140 and 168 Using Prime Factorisation Method
The prime factorisation of 140 and 168, respectively, is given by:
140 = (2 × 2 × 5 × 7) = 22 × 51 × 71 and
168 = (2 × 2 × 2 × 3 × 7) = 23 × 31 × 71
LCM (140, 168) = 840
LCM of 140 and 168 Using Division Method
We’ll divide the numbers (140, 168) by their prime factors to get the LCM of 140 and 168 using the division method (preferably common). The LCM of 140 and 168 is calculated by multiplying these divisors.
| 2 | 140 | 168 |
| 2 | 70 | 84 |
| 2 | 35 | 42 |
| 3 | 35 | 21 |
| 7 | 35 | 7 |
| 5 | 5 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (140, 168) = 840
LCM of 140 and 168 Using Listing the Multiples
To calculate the LCM of 140 and 168 by listing out the common multiples, list the multiples as shown below.
| Multiples of 140 | Multiples of 168 |
| 140 | 168 |
| 280 | 336 |
| 420 | 504 |
| 560 | 672 |
| 700 | 840 |
| 840 | 1008 |
The smallest common multiple of 140 and 168 is 840.
Therefore LCM (140, 168) = 840
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LCM of 140 and 168 Solved Example
Question: The GCD and LCM of two numbers are 28 and 840 respectively. If one number is 168, find the other number.
Solution:
Let the other number be p.
∵ GCD × LCM = 168 × p
⇒ p = (GCD × LCM)/168
⇒ p = (28 × 840)/168
⇒ p = 140
Therefore, the other number is 140.
Frequently Asked Questions on LCM of 140 and 168
What is the LCM of 140 and 168?
List the methods used to find the LCM of 140 and 168.
If the LCM of 168 and 140 is 840, Find its GCF.
Since the LCM of 168 and 140 = 840
⇒ 840 × GCF(168, 140) = 23520
Therefore, the greatest common factor = 23520/840 = 28.
How to Find the LCM of 140 and 168 by Prime Factorization?
⇒ LCM of 140, 168 = 23 × 3 × 5 × 7 = 840.
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