4 Per 9 2 Per 9

4 Per 9 2 Per 9

LCM of 4 and 9

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

LCM of 4 and 9 by Listing Multiples Method

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.

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LCM of 4 and 9 by Division Method

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.

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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.

4 Per 9 2 Per 9

Sumber: https://www.cuemath.com/numbers/lcm-of-4-and-9/

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