LCM of 9 and 72 is 72. In Maths, the LCM of any two numbers is the value which is evenly divisible by the given two numbers. The least common multiple of 9 and 72 is the smallest number we get among the common multiples. The LCM can be found easily by using various methods like prime factorisation, division and by listing the multiples. The smallest positive integer that divides 9 and 72 without leaving a remainder is the lcm of 9 and 72. It is the least common multiple of 9 and 72 when written out. The lcm of 9 and 72, as well as three techniques for computing it, can be found here.
Also read: Least common multiple
What is LCM of 9 and 72?
The answer to this question is 72. The LCM of 9 and 72 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 9 and 72, is the smallest positive integer 72 which is divisible by both 9 and 72 with no remainder.
How to Find LCM of 9 and 72?
LCM of 9 and 72 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 9 and 72 Using Prime Factorisation Method
The prime factorisation of 9 and 72, respectively, is given by:
9 = 3 x 3 = 3²
72 = 2 x 2 x 2 x 3 x 3 = 23 x 3²
LCM (9, 72) = 72
LCM of 9 and 72 Using Division Method
We’ll divide the numbers (9, 72) by their prime factors to get the LCM of 9 and 72 using the division method (preferably common). The LCM of 9 and 72 is calculated by multiplying these divisors.
| 2 | 9 | 72 |
| 2 | 9 | 36 |
| 2 | 9 | 18 |
| 3 | 9 | 9 |
| 3 | 3 | 3 |
| x | 1 | 1 |
No further division can be done.
Hence, LCM (9, 72) = 72
LCM of 9 and 72 Using Listing the Multiples
To calculate the LCM of 9 and 72 by listing out the common multiples, list the multiples as shown below
| Multiples of 9 | Multiples of 72 |
| 9 | 72 |
| 18 | 144 |
| 27 | 216 |
| …. | 288 |
| 72 | 360 |
The smallest common multiple of 9 and 72 is 72.
Therefore LCM (9, 72) = 72
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LCM of 9 and 72 Solved Example
Question: How do you calculate 72 divided by 9?
Solution: 72 divided by 9 is 8. By our rule relating division and multiplication, we have the following: If 72 ÷ 9 = c, then 72 = c × 9.
Frequently Asked Questions on LCM of 9 and 72
What is the LCM of 9 and 72?
List the methods used to find the LCM of 9 and 72.
What are the Factors of 9?
How to Find the LCM of 9 and 72?
Step 1: Find the prime factorization of 9
9 = 3 x 3
Step 2: Find the prime factorization of 72
72 = 2 x 2 x 2 x 3 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 72 = 2 x 2 x 2 x 3 x 3
Step 4: Therefore, the least common multiple of 9 and 72 is 72.
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