LCM of 9, 10 and 28 is 1260. The number divisible by 9, 10 and 28 evenly is the LCM. The common multiples of the numbers helps to find the least common multiple of 9, 10 and 28. The multiples of 9 are (9, 18, 27, 36, 45, 54, ….), the multiples of 10 are (10, 20, 30, 40, 50, ……) and the multiples of 28 are (28, 56, 84, 112, 140, ….) respectively. The LCM value can be determined effortlessly using prime factorisation, division and by listing out the multiples.
Also read: Least common multiple
What is LCM of 9, 10 and 28?
The answer to this question is 1260. The LCM of 9, 10 and 28 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9, 10 and 28, is the smallest positive integer 1260 which is divisible by both 9, 10 and 28 with no remainder.
How to Find LCM of 9, 10 and 28?
LCM of 9, 10 and 28 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9, 10 and 28 Using Prime Factorisation Method
The prime factorisation of 9, 10 and 28, respectively, is given by:
9 = 3 x 3 = 3²
10 = 2 x 5 = 2¹ x 5¹
28 = 2 x 2 x 7 = 2² x 7¹
LCM (9, 10, 28) = 1260
LCM of 9, 10 and 28 Using Division Method
We’ll divide the numbers (9, 10, 28) by their prime factors to get the LCM of 9, 10 and 28 using the division method (preferably common). The LCM of 9, 10 and 28 is calculated by multiplying these divisors.
|
2 |
9 |
10 |
28 |
|
2 |
9 |
5 |
14 |
|
3 |
9 |
5 |
7 |
|
3 |
3 |
5 |
7 |
|
5 |
1 |
5 |
7 |
|
7 |
1 |
1 |
7 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (9, 10, 28) = 1260
LCM of 9, 10 and 28 Using Listing the Multiples
To calculate the LCM of 9, 10 and 28 by listing out the common multiples, list the multiples as shown below.
- Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, . . . ., 1233, 1242, 1251, 1260, . . . .
- Multiples of 10 = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, . . . ., 1230, 1240, 1250, 1260, . . . .
- Multiples of 28 = 28, 56, 84, 112, 140, 168, 196, 224, 252, 280, . . . ., 1204, 1232, 1260, . . . .
LCM (9, 10, 28) = 1260
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LCM of 9, 10 and 28 Solved Examples
Question: Which is the LCM of 9, 10 and 28 in the numbers 130, 1260, 400, 380?
Solution:
LCM is the value which is exactly divisible by the three numbers given.
The number 1260 satisfies this condition.
Hence, the LCM is 1260.
Frequently Asked Questions on LCM of 9, 10 and 28
Calculate the GCF if the LCM of 9, 10 and 28 is 1260.
We know that;
LCM x GCF = 9 x 10 x 28
As LCM (9, 10, 28) is 1260
1260 x GCF = 2520
GCF = 2520/1260 = 2
Calculate the LCM of 9, 10 and 28.
Show the relation between GCF and LCM of 9, 10 and 28.
The relation between GCF and LCM of 9, 10 and 28 is
LCM x GCF = 9 x 10 x 28
LCM x GCF = 2520
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