The product of two number is 324 if their LCM is 36 find their HCF

LCM of 36 and 54 is the smallest number among all common multiples of 36 and 54. The first few multiples of 36 and 54 are (36, 72, 108, 144, 180, 216, . . . ) and (54, 108, 162, 216, 270, 324, . . . ) respectively. There are 3 commonly used methods to find LCM of 36 and 54 - by prime factorization, by division method, and by listing multiples.

What is the LCM of 36 and 54?

Answer: LCM of 36 and 54 is 108.

Explanation:

The LCM of two non-zero integers, x(36) and y(54), is the smallest positive integer m(108) that is divisible by both x(36) and y(54) without any remainder.

Methods to Find LCM of 36 and 54

The methods to find the LCM of 36 and 54 are explained below.

• By Prime Factorization Method
• By Listing Multiples
• By Division Method

LCM of 36 and 54 by Prime Factorization

Prime factorization of 36 and 54 is (2 × 2 × 3 × 3) = 22 × 32 and (2 × 3 × 3 × 3) = 21 × 33 respectively. LCM of 36 and 54 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 33 = 108.
Hence, the LCM of 36 and 54 by prime factorization is 108.

LCM of 36 and 54 by Listing Multiples

To calculate the LCM of 36 and 54 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 36 (36, 72, 108, 144, 180, 216, . . . ) and 54 (54, 108, 162, 216, 270, 324, . . . . )
• Step 2: The common multiples from the multiples of 36 and 54 are 108, 216, . . .
• Step 3: The smallest common multiple of 36 and 54 is 108.

∴ The least common multiple of 36 and 54 = 108.

LCM of 36 and 54 by Division Method

To calculate the LCM of 36 and 54 by the division method, we will divide the numbers(36, 54) by their prime factors (preferably common). The product of these divisors gives the LCM of 36 and 54.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 36 and 54. Write this prime number(2) on the left of the given numbers(36 and 54), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (36, 54) 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 36 and 54 is the product of all prime numbers on the left, i.e. LCM(36, 54) by division method = 2 × 2 × 3 × 3 × 3 = 108.

☛ Also Check:

LCM of 36 and 54 Examples

1. Example 1: The GCD and LCM of two numbers are 18 and 108 respectively. If one number is 54, find the other number.

   Solution:

   Let the other number be y.
   ∵ GCD × LCM = 54 × y ⇒ y = (GCD × LCM)/54 ⇒ y = (18 × 108)/54 ⇒ y = 36

   Therefore, the other number is 36.

Show Solution >

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The LCM of 36 and 54 is 108. To find the LCM of 36 and 54, we need to find the multiples of 36 and 54 (multiples of 36 = 36, 72, 108, 144; multiples of 54 = 54, 108, 162, 216) and choose the smallest multiple that is exactly divisible by 36 and 54, i.e., 108.

Which of the following is the LCM of 36 and 54? 108, 35, 21, 27

The value of LCM of 36, 54 is the smallest common multiple of 36 and 54. The number satisfying the given condition is 108.

What is the Relation Between GCF and LCM of 36, 54?

The following equation can be used to express the relation between GCF and LCM of 36 and 54, i.e. GCF × LCM = 36 × 54.

If the LCM of 54 and 36 is 108, Find its GCF.

LCM(54, 36) × GCF(54, 36) = 54 × 36 Since the LCM of 54 and 36 = 108 ⇒ 108 × GCF(54, 36) = 1944

Therefore, the GCF (greatest common factor) = 1944/108 = 18.

What is the Least Perfect Square Divisible by 36 and 54?

The least number divisible by 36 and 54 = LCM(36, 54)
LCM of 36 and 54 = 2 × 2 × 3 × 3 × 3 [Incomplete pair(s): 3]
⇒ Least perfect square divisible by each 36 and 54 = LCM(36, 54) × 3 = 324 [Square root of 324 = √324 = ±18]
Therefore, 324 is the required number.