LCM of 5 and 9 is the smallest number among all common multiples of 5 and 9. The first few multiples of 5 and 9 are (5, 10, 15, 20, 25, 30, . . . ) and (9, 18, 27, 36, 45, 54, 63, . . . ) respectively. There are 3 commonly used methods to find LCM of 5 and 9 - by division method, by listing multiples, and by prime factorization.
| 1. | LCM of 5 and 9 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 5 and 9?
Answer: LCM of 5 and 9 is 45.
Explanation:
The LCM of two non-zero integers, x(5) and y(9), is the smallest positive integer m(45) that is divisible by both x(5) and y(9) without any remainder.
Methods to Find LCM of 5 and 9
Let's look at the different methods for finding the LCM of 5 and 9.
- By Prime Factorization Method
- By Division Method
- By Listing Multiples
LCM of 5 and 9 by Prime Factorization
Prime factorization of 5 and 9 is (5) = 51 and (3 × 3) = 32 respectively. LCM of 5 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 32 × 51 = 45.
Hence, the LCM of 5 and 9 by prime factorization is 45.
LCM of 5 and 9 by Division Method
To calculate the LCM of 5 and 9 by the division method, we will divide the numbers(5, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 5 and 9.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 5 and 9. Write this prime number(3) on the left of the given numbers(5 and 9), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (5, 9) is a multiple of 3, divide it by 3 and write the quotient below it. Bring down any number that is not divisible by the prime number.
- Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 5 and 9 is the product of all prime numbers on the left, i.e. LCM(5, 9) by division method = 3 × 3 × 5 = 45.
LCM of 5 and 9 by Listing Multiples
To calculate the LCM of 5 and 9 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 5 (5, 10, 15, 20, 25, 30, . . . ) and 9 (9, 18, 27, 36, 45, 54, 63, . . . . )
- Step 2: The common multiples from the multiples of 5 and 9 are 45, 90, . . .
- Step 3: The smallest common multiple of 5 and 9 is 45.
∴ The least common multiple of 5 and 9 = 45.
☛ Also Check:
- LCM of 16 and 64 - 64
- LCM of 4, 5 and 10 - 20
- LCM of 45 and 54 - 270
- LCM of 35, 12 and 70 - 420
- LCM of 144 and 169 - 24336
- LCM of 8 and 36 - 72
- LCM of 15 and 27 - 135
FAQs on LCM of 5 and 9
What is the LCM of 5 and 9?
The LCM of 5 and 9 is 45. To find the least common multiple of 5 and 9, we need to find the multiples of 5 and 9 (multiples of 5 = 5, 10, 15, 20 . . . . 45; multiples of 9 = 9, 18, 27, 36 . . . . 45) and choose the smallest multiple that is exactly divisible by 5 and 9, i.e., 45.
What is the Least Perfect Square Divisible by 5 and 9?
The least number divisible by 5 and 9 = LCM(5, 9)
LCM of 5 and 9 = 3 × 3 × 5 [Incomplete pair(s): 5]
⇒ Least perfect square divisible by each 5 and 9 = LCM(5, 9) × 5 = 225 [Square root of 225 = √225 = ±15]
Therefore, 225 is the required number.
How to Find the LCM of 5 and 9 by Prime Factorization?
To find the LCM of 5 and 9 using prime factorization, we will find the prime factors, (5 = 5) and (9 = 3 × 3). LCM of 5 and 9 is the product of prime factors raised to their respective highest exponent among the numbers 5 and 9.
⇒ LCM of 5, 9 = 32 × 51 = 45.
What are the Methods to Find LCM of 5 and 9?
The commonly used methods to find the LCM of 5 and 9 are:
- Prime Factorization Method
- Division Method
- Listing Multiples
If the LCM of 9 and 5 is 45, Find its GCF.
LCM(9, 5) × GCF(9, 5) = 9 × 5
Since the LCM of 9 and 5 = 45
⇒ 45 × GCF(9, 5) = 45
Therefore, the GCF = 45/45 = 1.
