LCM of 18 and 72 is 72. LCM is the method we use to find the smallest common multiple lying between the numbers 18 and 72. Least common multiples of 18 and 72 can be obtained by knowing the common multiples of the two numbers. (18, 36, 54, 72, 90, 108, 126, ….) and (72, 144, 216, 288, 360, ….) are the multiples of 18 and 72. Students can find the LCM of two numbers by listing the multiples, prime factorization and division methods.
Also read: Least common multiple
What is LCM of 18 and 72?
The answer to this question is 72. The LCM of 18 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 18 and 72, is the smallest positive integer 72 which is divisible by both 18 and 72 with no remainder.
How to Find LCM of 18 and 72?
LCM of 18 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 18 and 72 Using Prime Factorisation Method
The prime factorisation of 18 and 72, respectively, is given by:
18 = 2 x 3 x 3 = 2¹ x 3²
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
LCM (18, 72) = 72
LCM of 18 and 72 Using Division Method
We’ll divide the numbers (18, 72) by their prime factors to get the LCM of 18 and 72 using the division method (preferably common). The LCM of 18 and 72 is calculated by multiplying these divisors.
|
2 |
18 |
72 |
|
2 |
9 |
36 |
|
2 |
9 |
18 |
|
3 |
9 |
9 |
|
3 |
3 |
3 |
|
x |
1 |
1 |
No further division can be done.
Hence, LCM (18, 72) = 72
LCM of 18 and 72 Using Listing the Multiples
To calculate the LCM of 18 and 72 by listing out the common multiples, list the multiples as shown below
Multiples of 18 = 18, 36, 54, 72, 90, 108, ….
Multiples of 72 = 72, 144, 216, 288, 360, 432, ….
LCM (18, 72) = 72
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 18 and 72 Solved Examples
Question: What is the smallest number exactly divisible by 18 and 72?
Solution:
We know that
LCM is the smallest number exactly divisible by 18 and 72.
(18, 36, 54, 72, 90, 108, ….) are the multiples of 18
(72, 144, 216, 288, 360, 432, ….) are the multiples of 72
Hence, the LCM of 18 and 72 is 72.
Frequently Asked Questions on LCM of 18 and 72
Mention the methods used to find the LCM of 18 and 72.
The methods used to find the LCM of 18 and 72 are
Prime Factorisation
Division method
Listing the multiples
Using prime factorisation, find the LCM of 18 and 72.
To find the LCM, the factors must be known
18 = 2 x 3 x 3
72 = 2 x 2 x 2 x 3 x 3
LCM is the product of prime factors raised to the highest exponent among 18 and 72.
LCM of 18, 72 = 72
What is the GCF if the LCM of 18 and 72 is 72?
LCM x GCF = 18 x 72
As the LCM = 72
72 x GCF = 1296
GCF = 1296/72 = 18
The LCM and GCD of two numbers are 72 and 18. If 72 is one number, determine the other.
Consider a as the other number
GCD x LCM = 72 x m
m = (GCD x LCM)/ 72
m = (18 x 72)/ 72
m = 18
Hence, the other number is 18.
Write the relation between LCM and GCF of 18 and 72.
The relation between LCM and GCF of 18 and 72 is
LCM x GCF = 18 x 72
LCM x GCF = 1296
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