LCM of 7 and 24 is 168. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. LCM of 7 and 24 is the smallest number among all common multiples of 7 and 24. The first few multiples of 7 and 24 are (7, 14, 21, 28, 35, 42, . . . ) and (24, 48, 72, 96, 120, . . . ) respectively.
Also read: Least common multiple
What is LCM of 7 and 24?
The answer to this question is 168. The LCM of 7 and 24 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 7 and 24, is the smallest positive integer 168 which is divisible by both 7 and 24 with no remainder.
How to Find LCM of 7 and 24?
LCM of 7 and 24 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 7 and 24 Using Prime Factorisation Method
The prime factorisation of 7 and 24, respectively, is given by:
(7) = 71 and
24 = (2 × 2 × 2 × 3) = 23 × 31
LCM (7, 24) = 168
LCM of 7 and 24 Using Division Method
We’ll divide the numbers (7, 24) by their prime factors to get the LCM of 7 and 24 using the division method (preferably common). The LCM of 7 and 24 is calculated by multiplying these divisors.
| 2 | 7 | 24 |
| 2 | 7 | 12 |
| 2 | 7 | 6 |
| 3 | 7 | 3 |
| 7 | 7 | 1 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (7, 24) = 168
LCM of 7 and 24 Using Listing the Multiples
To calculate the LCM of 7 and 24 by listing out the common multiples, list the multiples as shown below
| Multiples of 7 | Multiples of 24 |
| 7 | 24 |
| 14 | 48 |
| 21 | 72 |
| …. | ….. |
| 168 | 168 |
The smallest common multiple of 7 and 24 is 72.
Therefore LCM (7, 24) = 168
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LCM of 7 and 24 Solved Example
Question: The GCD and LCM of two numbers are 1 and 168 respectively. If one number is 7, find the other number.
Solution:
Let the other number be b.
∵ GCD × LCM = 7 × b
⇒ b = (GCD × LCM)/7
⇒ b = (1 × 168)/7
⇒ b = 24
Therefore, the other number is 24.
Frequently Asked Questions on LCM of 7 and 24
What is the LCM of 7 and 24?
List the methods used to find the LCM of 7 and 24.
If the LCM of 24 and 7 is 168, Find its GCF.
Since the LCM of 24 and 7 = 168
⇒ 168 × GCF(24, 7) = 168
Therefore, the greatest common factor (GCF) = 168/168 = 1.
How to Find the LCM of 7 and 24 by Prime Factorization?
⇒ LCM of 7, 24 = 168.
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