LCM of 4 and 9 is the smallest number among all common multiples of 4 and 9. The first few multiples of 4 and 9 are (4, 8, 12, 16, 20, 24, 28, . . . ) and (9, 18, 27, 36, . . . ) respectively. There are 3 commonly used methods to find LCM of 4 and 9 - by prime factorization, by listing multiples, and by division method.
| 1. | LCM of 4 and 9 |
| 2. | List of Methods |
| 3. | Solved Examples |
| 4. | FAQs |
What is the LCM of 4 and 9?
Answer: LCM of 4 and 9 is 36.
Explanation:
The LCM of two non-zero integers, x(4) and y(9), is the smallest positive integer m(36) that is divisible by both x(4) and y(9) without any remainder.
Methods to Find LCM of 4 and 9
The methods to find the LCM of 4 and 9 are explained below.
- By Listing Multiples
- By Prime Factorization Method
- By Division Method
LCM of 4 and 9 by Listing Multiples
To calculate the LCM of 4 and 9 by listing out the common multiples, we can follow the given below steps:
- Step 1: List a few multiples of 4 (4, 8, 12, 16, 20, 24, 28, . . . ) and 9 (9, 18, 27, 36, . . . . )
- Step 2: The common multiples from the multiples of 4 and 9 are 36, 72, . . .
- Step 3: The smallest common multiple of 4 and 9 is 36.
∴ The least common multiple of 4 and 9 = 36.
LCM of 4 and 9 by Prime Factorization
Prime factorization of 4 and 9 is (2 × 2) = 22 and (3 × 3) = 32 respectively. LCM of 4 and 9 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 32 = 36.
Hence, the LCM of 4 and 9 by prime factorization is 36.
LCM of 4 and 9 by Division Method
To calculate the LCM of 4 and 9 by the division method, we will divide the numbers(4, 9) by their prime factors (preferably common). The product of these divisors gives the LCM of 4 and 9.
- Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 4 and 9. Write this prime number(2) on the left of the given numbers(4 and 9), separated as per the ladder arrangement.
- Step 2: If any of the given numbers (4, 9) is a multiple of 2, divide it by 2 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 4 and 9 is the product of all prime numbers on the left, i.e. LCM(4, 9) by division method = 2 × 2 × 3 × 3 = 36.
☛ Also Check:
- LCM of 21 and 35 - 105
- LCM of 63 and 81 - 567
- LCM of 24 and 27 - 216
- LCM of 2, 4 and 7 - 28
- LCM of 12, 15 and 45 - 180
- LCM of 39 and 65 - 195
- LCM of 30, 36 and 40 - 360
FAQs on LCM of 4 and 9
What is the LCM of 4 and 9?
The LCM of 4 and 9 is 36. To find the least common multiple (LCM) of 4 and 9, we need to find the multiples of 4 and 9 (multiples of 4 = 4, 8, 12, 16 . . . . 36; multiples of 9 = 9, 18, 27, 36) and choose the smallest multiple that is exactly divisible by 4 and 9, i.e., 36.
How to Find the LCM of 4 and 9 by Prime Factorization?
To find the LCM of 4 and 9 using prime factorization, we will find the prime factors, (4 = 2 × 2) and (9 = 3 × 3). LCM of 4 and 9 is the product of prime factors raised to their respective highest exponent among the numbers 4 and 9.
⇒ LCM of 4, 9 = 22 × 32 = 36.
What is the Relation Between GCF and LCM of 4, 9?
The following equation can be used to express the relation between GCF and LCM of 4 and 9, i.e. GCF × LCM = 4 × 9.
If the LCM of 9 and 4 is 36, Find its GCF.
LCM(9, 4) × GCF(9, 4) = 9 × 4
Since the LCM of 9 and 4 = 36
⇒ 36 × GCF(9, 4) = 36
Therefore, the greatest common factor (GCF) = 36/36 = 1.
What is the Least Perfect Square Divisible by 4 and 9?
The least number divisible by 4 and 9 = LCM(4, 9)
LCM of 4 and 9 = 2 × 2 × 3 × 3 [No incomplete pair]
⇒ Least perfect square divisible by each 4 and 9 = 36 [Square root of 36 = √36 = ±6]
Therefore, 36 is the required number.
