LCM of 78 and 104 is 312. The number which is evenly divisible from the two given numbers is the LCM. The least common multiple of 78 and 104 can be found using the common multiples. The multiples of 78 are (78, 156, 234, 312, ….) and the multiples of 104 are (104, 208, 312, 416, 520, 624, ….) respectively. The methods we can use to find the LCM are prime factorisation, division and by listing the multiples.
Also read: Least common multiple
What is LCM of 78 and 104?
The answer to this question is 312. The LCM of 78 and 104 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 78 and 104, is the smallest positive integer 312 which is divisible by both 78 and 104 with no remainder.
How to Find LCM of 78 and 104?
LCM of 78 and 104 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 78 and 104 Using Prime Factorisation Method
The prime factorisation of 78 and 104, respectively, is given by:
78 = 2 x 3 x 13 = 2¹ x 3¹ x 13¹
104 = 2 x 2 x 2 x 13 = 2³ x 13¹
LCM (78, 104) = 312
LCM of 78 and 104 Using Division Method
We’ll divide the numbers (78, 104) by their prime factors to get the LCM of 78 and 104 using the division method (preferably common). The LCM of 78 and 104 is calculated by multiplying these divisors.
|
2 |
78 |
104 |
|
2 |
39 |
52 |
|
2 |
39 |
26 |
|
3 |
39 |
13 |
|
13 |
13 |
13 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (78, 104) = 312
LCM of 78 and 104 Using Listing the Multiples
To calculate the LCM of 78 and 104 by listing out the common multiples, list the multiples as shown below
|
Multiples of 78 |
Multiples of 104 |
|
78 |
104 |
|
156 |
208 |
|
234 |
312 |
|
312 |
416 |
LCM (78, 104) = 312
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Video Lesson on Applications of LCM
LCM of 78 and 104 Solved Examples
Question: The LCM and GCD of two numbers are 312 and 26 respectively. If one number is 78, what is the other number?
Solution:
Consider the number as z
We know that
GCD x LCM = 78 x z
z = (GCD x LCM)/78
Substituting the values
z = (26 x 312)/78
z = 104
Hence, the other number is 104.
Frequently Asked Questions on LCM of 78 and 104
If the LCM of 78 and 104 is 312, calculate its GCF.
We know that
LCM x GCF = 78 x 104
As LCM (78, 104) is 312
312 x GCF = 8112
GCF = 8112/312 = 26
Find the LCM of 78 and 104.
Show the relation between GCF and LCM of 78 and 104.
The relation between GCF and LCM of 78 and 104 is
LCM x GCF = 78 x 104
LCM x GCF = 8112
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