LCM of 40 and 70 is 280. Students will understand the LCM concept effectively by going through this article. The least common multiple of 40 and 70 is the value we get from the common multiples. The multiples of 40 are (40, 80, 120, 160, 200, 240, ….) and the multiples of 70 are (70, 140, 210, 280, 350, 420, ….) respectively. We can make use of prime factorisation, division and by listing the multiples to find the LCM value.
Also read: Least common multiple
What is LCM of 40 and 70?
The answer to this question is 280. The LCM of 40 and 70 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 40 and 70, is the smallest positive integer 280 which is divisible by both 40 and 70 with no remainder.
How to Find LCM of 40 and 70?
LCM of 40 and 70 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 40 and 70 Using Prime Factorisation Method
The prime factorisation of 40 and 70, respectively, is given by:
40 = 2 x 2 x 2 x 5 = 2³x 5¹
70 = 2 x 5 x 7 = 2¹ x 5¹ x 7¹
LCM (40, 70) = 280
LCM of 40 and 70 Using Division Method
We’ll divide the numbers (40, 70) by their prime factors to get the LCM of 40 and 70 using the division method (preferably common). The LCM of 40 and 70 is calculated by multiplying these divisors.
|
2 |
40 |
70 |
|
2 |
20 |
35 |
|
2 |
10 |
35 |
|
5 |
5 |
35 |
|
7 |
1 |
7 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (40, 70) = 280
LCM of 40 and 70 Using Listing the Multiples
To calculate the LCM of 40 and 70 by listing out the common multiples, list the multiples as shown below.
|
Multiples of 40 |
Multiples of 70 |
|
40 |
70 |
|
80 |
140 |
|
120 |
210 |
|
160 |
280 |
|
200 |
350 |
|
240 |
420 |
|
280 |
490 |
|
320 |
560 |
LCM (40, 70) = 280
Related Articles
Video Lesson on Applications of LCM
LCM of 40 and 70 Solved Examples
Question: The LCM and GCD of two numbers are 280 and 10 respectively. If one number is 70, what is the other number?
Solution:
Consider the number as z.
We know that;
GCD x LCM = 70 x z
z = (GCD x LCM)/70
Substituting the values
z = (10 x 280)/70
z = 40
Hence, the other number is 40.
Frequently Asked Questions on LCM of 40 and 70
Calculate the GCF, if the LCM of 40 and 70 is 280.
We know that
LCM x GCF = 40 x 70
As LCM (40, 70) is 280
280 x GCF = 2800
GCF = 2800/280 = 10
Determine the LCM of 40 and 70.
The LCM of 40 and 70 is 280. To find the LCM, the multiples of 40 and 70 has to be obtained
(40, 80, 120, 160, 200, 240, 280, ….) are the multiples of 40
(70, 140, 210, 280, 350, …..) are the multiples of 70
The smallest multiple exactly divisible by 40 and 70 is 280.
Write the relation between GCF and LCM of 40 and 70.
The relation between GCF and LCM of 40 and 70 is
LCM x GCF = 40 x 70
LCM x GCF = 2800
If the GCD and product of two numbers is 10 and 2800, find the LCM.
Given
GCD = 10
Product = 2800
LCM x GCD = Product
LCM = Product/GCD
LCM = 2800/10 = 280
Hence, the LCM is 280.
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