LCM of 24 and 26 is 312. The LCM of any two integers in mathematics is the value that is evenly divisible by the two values. The smallest number among all common multiples of 5 and 100 is the LCM of 5 and 100. (5, 10, 15, 20, 25, 30,…) and (100, 200, 300, 400, 500, 600, 700,…) are the first few multiples of 5 and 100, respectively. To find the LCM of 5 and 100, there are three main methods: listing multiples, prime factorization, and division technique.
Also read: Least common multiple
What is LCM of 24 and 26?
The answer to this question is 312. The LCM of 24 and 26 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 24 and 26, is the smallest positive integer 312 which is divisible by both 24 and 26 with no remainder.
How to Find LCM of 24 and 26?
LCM of 24 and 26 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 24 and 26 Using Prime Factorisation Method
The prime factorisation of 24 and 26, respectively, is given by:
24 = (2 × 2 × 2 × 3) = 23 × 31 and
26 = (2 × 13) = 21 × 131
LCM (24, 26) = 312
LCM of 24 and 26 Using Division Method
We’ll divide the numbers (24, 26) by their prime factors to get the LCM of 24 and 26 using the division method (preferably common). The LCM of 24 and 26 is calculated by multiplying these divisors.
| 2 | 24 | 26 |
| 2 | 12 | 13 |
| 2 | 6 | 13 |
| 3 | 3 | 13 |
| 13 | 1 | 13 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (24, 26) = 312
LCM of 24 and 26 Using Listing the Multiples
To calculate the LCM of 24 and 26 by listing out the common multiples, list the multiples as shown below.
| Multiples of 24 | Multiples of 26 |
| 24 | 26 |
| 48 | 52 |
| 72 | 78 |
| … | …… |
| 312 | 312 |
The smallest common multiple of 24 and 26 is 72.
Therefore LCM (24, 26) = 312
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LCM of 24 and 26 Solved Example
Find the smallest number that is divisible by 24 and 26 exactly.
Solution:
The smallest number that is divisible by 24 and 26 exactly is their LCM.
⇒ Multiples of 24 and 26:
Multiples of 24 = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, . . . .
Multiples of 26 = 26, 52, 78, 104, 130, 156, 182, 208, 234, 260, 286, 312, . . . .
Therefore, the LCM of 24 and 26 is 312.
Frequently Asked Questions on LCM of 24 and 26
What is the LCM of 24 and 26?
List the methods used to find the LCM of 24 and 26.
If the LCM of 26 and 24 is 312, Find its GCF.
Since the LCM of 26 and 24 = 312
⇒ 312 × GCF(26, 24) = 624
Therefore, the GCF (greatest common factor) = 624/312 = 2.
What is the Least Perfect Square Divisible by 24 and 26?
LCM of 24 and 26 = 2 × 2 × 2 × 3 × 13 [Incomplete pair(s): 2, 3, 13] ⇒ Least perfect square divisible by each 24 and 26 = LCM(24, 26) × 2 × 3 × 13 = 24336 [Square root of 24336 = √24336 = ±156] Therefore, 24336 is the required number.
How to Find the LCM of 24 and 26 by Prime Factorization?
⇒ LCM of 24, 26 = 23 × 3 × 13 = 312.
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