LCM of 60 and 68 is 1020. In the multiples of 60 and 68, the value divisible evenly is the LCM. Least common multiple of 60 and 68 is the common among two numbers which we get by multiplication. (60, 120, 180, 240, 300, 360, ….) and (68, 136, 204, 272, ….) are the multiples of 60 and 68. The LCM of two numbers can be found by the listing of multiples, prime factorization and division.
Also read: Least common multiple
What is LCM of 60 and 68?
The answer to this question is 1020. The LCM of 60 and 68 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 60 and 68, is the smallest positive integer 1020 which is divisible by both 60 and 68 with no remainder.
How to Find LCM of 60 and 68?
LCM of 60 and 68 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 68 Using Prime Factorisation Method
The prime factorisation of 60 and 68, respectively, is given by:
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
68 = 2 x 2 x 17 = 2² x 17¹
LCM (60, 68) = 1020
LCM of 60 and 68 Using Division Method
We’ll divide the numbers (60, 68) by their prime factors to get the LCM of 60 and 68 using the division method (preferably common). The LCM of 60 and 68 is calculated by multiplying these divisors.
|
2 |
60 |
68 |
|
2 |
30 |
34 |
|
3 |
15 |
17 |
|
5 |
5 |
17 |
|
17 |
1 |
17 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (60, 68) = 1020
LCM of 60 and 68 Using Listing the Multiples
To calculate the LCM of 60 and 68 by listing out the common multiples, list the multiples as shown below:
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, . . . ., 900, 960, 1020, . . . .
Multiples of 68 = 68, 136, 204, 272, 340, 408, 476, 544, 612, 680, . . . ., 748, 816, 884, 952, 1020, . . . .
LCM (60, 68) = 1020
Related Articles
- Prime Factorization and Division Method for LCM and HCF
- Prime Factors
- Properties of HCF and LCM
- LCM Formula
Video Lesson on Applications of LCM
LCM of 60 and 68 Solved Examples
Question: If the GCD is 4 and the product of two numbers is 4080, find the LCM.
Solution:
Given,
GCD = 4
Product = 4080
LCM x GCD = Product
LCM = Product/GCD
LCM = 4080/4
LCM = 1020
Hence, the LCM of 60 and 68 is 1020.
Frequently Asked Questions on LCM of 60 and 68
What are the methods used to find the LCM of 60 and 68?
The methods used to find the LCM of 60 and 68 are:
Prime Factorisation
Division method
Listing the multiples
Using the prime factorisation method, determine the LCM of 60 and 68.
We should first know the factors to determine the LCM
60 = 2 x 2 x 3 x 5
68 = 2 x 2 x 17
LCM is the product of prime factors raised to the highest exponent among 60 and 68.
LCM of 60 and 68 = 1020
Find the GCF if the LCM of 60 and 68 is 1020.
LCM x GCF = 60 x 68
As the LCM = 1020
1020 x GCF = 4080
GCF = 4080/1020 = 4
Show the relation between LCM and GCF of 60 and 68.
The relation between LCM and GCF of 60 and 68 is
GCF x LCM = 60 x 68
GCF x LCM = 4080
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