The Least Common Multiple (LCM) of two numbers (9 and 18) is the smallest number that is a multiple of both numbers.
In simple words, it is the smallest number that can be divided by both numbers by 9 and 18 without leaving a remainder, that is called a least common multiple of 9 and 18.
How to Least Common Multiple of 9 and 18?
To find the LCM (Least Common Multiple) of 9 and 18, you can use the following steps:
List the multiples of each number:
- Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …
- Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, 180, …
Find the smallest multiple that is common to both lists:
The smallest multiple that is common to both lists is 18. Therefore, the LCM of 9 and 18 is 18.
Answer: Least Common Multiple of 9 and 18 is 18.
Another way to find the LCM of 9 and 18 is by using the formula:
LCM(9, 18) = (9 x 18) / GCD(9, 18)
where GCD(9, 18) is the Greatest Common Divisor (GCD) of 9 and 18. Using this formula, we can calculate the LCM as follows:
LCM(9, 18) = (9 x 18) / GCD(9, 18) = 162 / 9 = 18
Note that GCD (9,18) = 9
Using prime factorization method
Factorize the numbers into their prime factors 9 = 3^2 18 = 2*3^2
Take the highest power of each prime factor 3^2
Multiply all the prime factors together, it will give the LCM LCM(9, 18) = 36
Find Least Common Multiple of 9 and 18 with GCF Formula
The formula of Least Common Multiple LCM is LCM(a,b) = ( a × b) / GCF(a,b).
- GCF(9,18) = 9
- LCM(9,18) = ( 9 × 18) / 9
- LCM(9,18) = 162 / 9
- LCM(9,18) = 18
How to Find Least Common Multiple (LCM) of 9 and 18 with Primes?
By multiplying the greatest exponent prime factors of 9 and 18, the least common multiple may be calculated.
So, to calculate the Least Common Multiple of 9 and 18 you need to calculate the prime factors of 9 and 18.
- Prime Factorization of 9 = 32
- Prime Factorization of 18 = 21 × 32
Now, By multiply highest exponent prime factors of 9 & 18 number. By this you can get the LCM of 9 and 18.
- LCM(9,18) = 32 × 21
- LCM(9,18) = 18
Hence, the least common multiple (LCM) of 9 and 18 is 18. It can be calculated using different methods like listing multiples, using formula and prime factorization method.
Rakesh Sharma
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