LCM of 60 and 700 is 2100. The smallest number that evenly divides 60 and 700 provides the LCM value. The common multiples between the two numbers will help you obtain the least common multiple of 60 and 700. The multiples of 60 are (60, 120, 180, 240, 300, ….) and the multiples of 700 are (700, 1400, 2100, 2800, 3500, …..) respectively. For a clear knowledge of the LCM concept and methods like prime factorisation, division and listing out the multiples kindly visit BYJU’S.
Also read: Least common multiple
What is LCM of 60 and 700?
The answer to this question is 2100. The LCM of 60 and 700 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 60 and 700, is the smallest positive integer 2100 which is divisible by both 60 and 700 with no remainder.
How to Find LCM of 60 and 700?
LCM of 60 and 700 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 60 and 700 Using Prime Factorisation Method
The prime factorisation of 60 and 700, respectively, is given by:
60 = 2 x 2 x 3 x 5 = 2² x 3¹ x 5¹
700 = 2 x 2 x 5 x 5 x 7 = 2² x 5² x 7¹
LCM (60, 700) = 2100
LCM of 60 and 700 Using Division Method
We’ll divide the numbers (60, 700) by their prime factors to get the LCM of 60 and 700 using the division method (preferably common). The LCM of 60 and 700 is calculated by multiplying these divisors.
|
2 |
60 |
700 |
|
2 |
30 |
350 |
|
3 |
15 |
175 |
|
5 |
5 |
175 |
|
5 |
1 |
35 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (60, 700) = 2100
LCM of 60 and 700 Using Listing the Multiples
To calculate the LCM of 60 and 700 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, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, …..
Multiples of 700 = 700, 1400, 2100, 2800, 3500, …..
LCM (60, 700) = 2100
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LCM of 60 and 700 Solved Examples
Question: Calculate the smallest number divisible evenly by 60 and 700 exactly.
Solution:
The smallest number divisible by 60 and 700 exactly is LCM.
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, …..
Multiples of 700 = 700, 1400, 2100, 2800, 3500, ….
Therefore, the LCM of 60 and 700 is 2100.
Frequently Asked Questions on LCM of 60 and 700
Find the GCF if the LCM of 60 and 700 is 2100.
We know that,
LCM x GCF = 60 x 700
As LCM (60, 700) is 2100
2100 x GCF = 42000
GCF = 42000/2100 = 20
What is the LCM of 60 and 700?
The LCM of 60 and 700 is 2100. First the multiples of 60 and 700 have to be found to get the LCM value.
Multiples of 60 = 60, 120, 180, 240, 300, 360, 420, 480, 540, 600, 660, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1200, 1260, 1320, 1380, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1980, 2040, 2100, …..
Multiples of 700 = 700, 1400, 2100, 2800, 3500, ….
The smallest multiple exactly divisible by 60 and 700 is 2100.
Show the relation between GCF and LCM of 60 and 700.
The relation between GCF and LCM of 60 and 700 is
LCM x GCF = 60 x 700
LCM x GCF = 42000
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