Multiples Of 4 And 9

LCM of 4 and 9

LCM of 4 and nine is the smallest number amongst all common multiples of 4 and 9. The showtime few multiples of 4 and 9 are (four, viii, 12, xvi, 20, 24, 28, . . . ) and (9, eighteen, 27, 36, . . . ) respectively. There are 3 usually used methods to detect LCM of 4 and 9 - past prime number factorization, by listing multiples, and by division method.

1.	LCM of 4 and nine
ii.	Listing of Methods
three.	Solved Examples
4.	FAQs

What is the LCM of 4 and 9?

Reply: LCM of 4 and 9 is 36.

LCM of 4 and 9

Explanation:

The LCM of two not-naught integers, 10(4) and y(9), is the smallest positive integer thou(36) that is divisible past both x(4) and y(9) without any balance.

Methods to Find LCM of 4 and 9

The methods to find the LCM of 4 and ix are explained beneath.

By Listing Multiples
By Prime number Factorization Method
Past Division Method

LCM of 4 and ix by Listing Multiples

LCM of 4 and 9 by Listing Multiples Method

To summate the LCM of 4 and nine by listing out the common multiples, we tin can follow the given below steps:

Step 1: List a few multiples of 4 (iv, 8, 12, xvi, 20, 24, 28, . . . ) and ix (ix, eighteen, 27, 36, . . . . )
Step two: The mutual multiples from the multiples of 4 and 9 are 36, 72, . . .
Step 3: The smallest mutual 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 number factorization of four and 9 is (2 × 2) = 2² and (3 × iii) = 3² respectively. LCM of four and nine can be obtained by multiplying prime factors raised to their respective highest power, i.east. twoⁱⁱ × 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 past the division method, we will divide the numbers(4, nine) by their prime number factors (preferably common). The product of these divisors gives the LCM of 4 and nine.

Step one: Find the smallest prime number that is a factor of at least one of the numbers, iv and nine. Write this prime(2) on the left of the given numbers(4 and 9), separated every bit per the ladder arrangement.
Step 2: If any of the given numbers (4, 9) is a multiple of two, divide information technology by 2 and write the quotient beneath it. Bring downwardly whatsoever number that is not divisible past the prime number.
Step 3: Continue the steps until only 1s are left in the concluding row.

The LCM of 4 and 9 is the product of all prime number numbers on the left, i.e. LCM(iv, ix) by partitioning 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, iv and seven - 28
LCM of 12, 15 and 45 - 180
LCM of 39 and 65 - 195
LCM of thirty, 36 and 40 - 360

FAQs on LCM of four and 9

What is the LCM of 4 and 9?

The LCM of 4 and 9 is 36 . To find the least mutual multiple (LCM) of 4 and 9, we need to detect the multiples of 4 and 9 (multiples of iv = 4, 8, 12, 16 . . . . 36; multiples of 9 = ix, 18, 27, 36) and choose the smallest multiple that is exactly divisible past four and ix, i.e., 36.

How to Detect the LCM of 4 and 9 by Prime number Factorization?

To find the LCM of 4 and 9 using prime number factorization, we volition detect the prime factors, (4 = 2 × 2) and (nine = iii × 3). LCM of iv and nine is the product of prime factors raised to their corresponding highest exponent amid the numbers 4 and 9.
⇒ LCM of 4, 9 = 2² × 3ⁱⁱ = 36.

What is the Relation Between GCF and LCM of iv, 9?

The following equation tin be used to express the relation between GCF and LCM of four and 9, i.eastward. GCF × LCM = 4 × ix.

If the LCM of 9 and 4 is 36, Observe its GCF.

LCM(ix, 4) × GCF(nine, four) = ix × 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 nine = ii × 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.