LCM of 8 and 36

LCM of 8 and 36 is the smallest number among all common multiples of 8 and 36. The first few multiples of 8 and 36 are (8, 16, 24, 32, 40, 48, . . . ) and (36, 72, 108, 144, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 36 - by listing multiples, by prime factorization, and by division method.

Answer: LCM of 8 and 36 is 72.

Explanation:

The LCM of two non-zero integers, x(8) and y(36), is the smallest positive integer m(72) that is divisible by both x(8) and y(36) without any remainder.

The methods to find the LCM of 8 and 36 are explained below.

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

LCM of 8 and 36 by Prime Factorization

Prime factorization of 8 and 36 is (2 × 2 × 2) = 2³ and (2 × 2 × 3 × 3) = 2² × 3² respectively. LCM of 8 and 36 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 2³ × 3² = 72.
Hence, the LCM of 8 and 36 by prime factorization is 72.

LCM of 8 and 36 by Listing Multiples

To calculate the LCM of 8 and 36 by listing out the common multiples, we can follow the given below steps:

• Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, 48, . . . ) and 36 (36, 72, 108, 144, . . . . )
• Step 2: The common multiples from the multiples of 8 and 36 are 72, 144, . . .
• Step 3: The smallest common multiple of 8 and 36 is 72.

∴ The least common multiple of 8 and 36 = 72.

LCM of 8 and 36 by Division Method

To calculate the LCM of 8 and 36 by the division method, we will divide the numbers(8, 36) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 36.

• Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 36. Write this prime number(2) on the left of the given numbers(8 and 36), separated as per the ladder arrangement.
• Step 2: If any of the given numbers (8, 36) 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 8 and 36 is the product of all prime numbers on the left, i.e. LCM(8, 36) by division method = 2 × 2 × 2 × 3 × 3 = 72.

☛ Also Check:

• LCM of 24 and 56 - 168
• LCM of 4 and 16 - 16
• LCM of 5 and 24 - 120
• LCM of 3 and 5 - 15
• LCM of 9 and 14 - 126
• LCM of 8, 10 and 12 - 120
• LCM of 18 and 36 - 36

FAQs on LCM of 8 and 36

What is the LCM of 8 and 36?

The LCM of 8 and 36 is 72. To find the LCM (least common multiple) of 8 and 36, we need to find the multiples of 8 and 36 (multiples of 8 = 8, 16, 24, 32 . . . . 72; multiples of 36 = 36, 72, 108, 144) and choose the smallest multiple that is exactly divisible by 8 and 36, i.e., 72.

What are the Methods to Find LCM of 8 and 36?

The commonly used methods to find the LCM of 8 and 36 are:

• Division Method
• Listing Multiples
• Prime Factorization Method

What is the Least Perfect Square Divisible by 8 and 36?

The least number divisible by 8 and 36 = LCM(8, 36)
LCM of 8 and 36 = 2 × 2 × 2 × 3 × 3 [Incomplete pair(s): 2]
⇒ Least perfect square divisible by each 8 and 36 = LCM(8, 36) × 2 = 144 [Square root of 144 = √144 = ±12]
Therefore, 144 is the required number.

What is the Relation Between GCF and LCM of 8, 36?

The following equation can be used to express the relation between GCF and LCM of 8 and 36, i.e. GCF × LCM = 8 × 36.

If the LCM of 36 and 8 is 72, Find its GCF.

LCM(36, 8) × GCF(36, 8) = 36 × 8
Since the LCM of 36 and 8 = 72
⇒ 72 × GCF(36, 8) = 288
Therefore, the GCF (greatest common factor) = 288/72 = 4.